A nonlift newform <i>f</i> in S

A nonlift newform in S₉(K(16))⁻

(Filename: eigs/eig-minus-9-16-4.html)

FORMULA FOR THE EIGENFORM f
with 3⁹⁻³λ₃ = -1920

Note that T(3) is the Hecke operator under the scalar-invariant slash and λ₃ is the corresponding eigenvalue.

The eigenform f has the formula
f = Σ_i=1⁷ b_i Grit(φ_i) + Σ_i=0¹⁴ c_i T(3)ⁱ g
where g is the Borcherds product that helped span the space S₉(K(16))⁻ and where φ_i are jacobi forms in J_9,16^cusp given by the following table.

φ₁	TB(9;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3)\|W₂
φ₂	TB(9;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,6)\|W₃
φ₃	TB(9;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4)\|W₃
φ₄	TB(9;1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3)\|W₃
φ₅	TB(9;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,10)\|W₅
φ₆	TB(9;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,5,5,6,6)\|W₅
φ₇	TB(9;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,5,9)\|W₅

Here is a table of the coefficients b_i and c_i.

b₁	-1360504024067065955984432306524336/22046522836835759668875
b₂	-1227247852164476821089517192043389472/27825861323349133810644375
b₃	-6318209842048253660736071725640885056/194781029263443936674510625
b₄	4249677879320668232621838082109245472/30299271218757945704923875
b₅	1472749161520910115063474596156748832/1623175243862032805620921875
b₆	694124036746135470775169951745860512/324635048772406561124184375
b₇	128318349592892432131159786818726592/108211682924135520374728125
c₀	6093264041148416/20727
c₁	172745803321344/11515
c₂	-4914108611058816/57575
c₃	-3332832200840628/287875
c₄	8114148324379836/1439375
c₅	10062117096208587/11515000
c₆	-3566237757145587/46060000
c₇	-14206488114530781/1473920000
c₈	0
c₉	0
c₁₀	0
c₁₁	0
c₁₂	0
c₁₃	0
c₁₄	0

COEFFICIENTS OF f (return to top)

Use the notation

[a b c ]

a	b
b	c

Here is a list of some Fourier coefficients of f.

2u det(2u) a(u, f)

[4 -53 704] 7 -2500608

[8 -89 992] 15 -49330176

[4 -25 160] 15 34326528

[12 -109 992] 23 100251648

[6 -13 32] 23 100251648

[6 -19 64] 23 -16594944

[14 -42 128] 28 -600145920

[14 -70 352] 28 -600145920

[8 -42 224] 28 -600145920

[8 -106 1408] 28 600145920

[16 -113 800] 31 -414191616

[8 -113 1600] 31 -414191616

[14 -47 160] 31 665161728

[20 -101 512] 39 -5943035904

[10 -91 832] 39 505350144

[10 -101 1024] 39 -505350144

[8 -27 96] 39 -3844798464

[24 -73 224] 47 -224145408

[12 -73 448] 47 1699958784

[4 9 32] 47 224145408

[8 -73 672] 47 1699958784

[16 -55 192] 47 3905040384

[2 4 32] 48 2778857472

[26 76 224] 48 2778857472

[6 12 32] 48 2778857472

[14 36 96] 48 2778857472

[2 3 32] 55 1353738240

[14 -29 64] 55 600827904

[14 -99 704] 55 -600827904

[8 -35 160] 55 -4114409472

[2 2 32] 60 -13177749504

[30 -210 1472] 60 -13177749504

[16 -50 160] 60 9576873984

[16 -178 1984] 60 -9576873984

[10 -30 96] 60 9576873984

[10 -50 256] 60 9576873984

[8 -50 320] 60 13177749504

[8 -114 1632] 60 -13177749504

[2 1 32] 63 -21791889408

[16 -225 3168] 63 -7069673472

[4 33 288] 63 7069673472

[12 -159 2112] 63 4801167360

[8 -97 1184] 63 -18865268736

[2 0 32] 64 0

[2 8 64] 64 -18739101696

[2 16 160] 64 0

[4 8 32] 64 -18739101696

[20 56 160] 64 -18739101696

[10 -24 64] 64 18739101696

[10 -64 416] 64 0

[10 -144 2080] 64 0

[36 -469 6112] 71 16178706432

[18 -181 1824] 71 9988110336

[18 -235 3072] 71 22136064000

[12 -85 608] 71 9988110336

[120 277 640] 71 -16178706432

[10 -43 192] 71 -3379230720

[10 -53 288] 71 -22136064000

[40 -441 4864] 79 -43846569984

[20 -121 736] 79 19481554944

[190 441 1024] 79 43846569984

[10 -71 512] 79 -19481554944

[10 -121 1472] 79 36045582336

[44 -397 3584] 87 18579744768

[22 -45 96] 87 -36800993280

[22 -243 2688] 87 -94874658816

[16 -115 832] 87 36800993280

[12 -51 224] 87 14966593536

[134 307 704] 87 18579744768

[46 -138 416] 92 -13352337408

[46 -230 1152] 92 -13352337408

[4 6 32] 92 13352337408

[24 -218 1984] 92 -13352337408

[26 70 192] 92 13352337408

[162 374 864] 92 -13352337408

[6 26 128] 92 -25398902784

[26 -86 288] 92 25398902784

[12 -26 64] 92 -13352337408

[12 -38 128] 92 25398902784

[12 -122 1248] 92 13352337408

[12 -134 1504] 92 -25398902784

[48 -337 2368] 95 87202793472

[24 -337 4736] 95 -35270621184

[4 17 96] 95 28494428160

[16 -81 416] 95 -28494428160

[6 49 416] 95 35270621184

[12 -145 1760] 95 24794892288

[60 145 352] 95 55766513664

[10 15 32] 95 87202793472

[52 -261 1312] 103 -16488327168

[4 5 32] 103 16488327168

[26 -261 2624] 103 26845845504

[14 -59 256] 103 65260185600

[14 -101 736] 103 26845845504

[56 -169 512] 111 -108406130688

[28 -169 1024] 111 35567056896

[120 297 736] 111 80632104960

[6 9 32] 111 108406130688

[14 -169 2048] 111 99146151936

[14 -183 2400] 111 -112447567872

[12 -87 640] 111 -35567056896

[10 23 64] 111 -80632104960

[2 4 64] 112 -96372523008

[58 172 512] 112 -96372523008

[4 4 32] 112 -96372523008

[28 -84 256] 112 -50572296192

[28 -140 704] 112 -50572296192

[28 -196 1376] 112 -96372523008

[14 -28 64] 112 96372523008

[14 -84 512] 112 96372523008

[8 12 32] 112 -96372523008

[16 -84 448] 112 -50572296192

[16 -148 1376] 112 96372523008

[16 -212 2816] 112 50572296192

[2 3 64] 119 42029764608

[30 -61 128] 119 72313491456

[30 -451 6784] 119 -42029764608

[20 -61 192] 119 111883112448

[90 221 544] 119 177652740096

[16 -67 288] 119 151133564928

[8 67 576] 119 72313491456

[12 -61 320] 119 111883112448

[24 61 160] 119 -164921462784

[12 -125 1312] 119 -177652740096

[2 2 64] 124 131530162176

[62 -434 3040] 124 131530162176

[4 2 32] 124 131530162176

[32 -226 1600] 124 131530162176

[16 -98 608] 124 -131530162176

[16 -226 3200] 124 131530162176

[8 34 160] 124 95390466048

[28 -94 320] 124 -95390466048

[10 14 32] 124 131530162176

[14 -46 160] 124 -95390466048

[14 -130 1216] 124 -131530162176

[14 -158 1792] 124 95390466048

[2 1 64] 127 282632355840

[4 1 32] 127 282632355840

[32 -449 6304] 127 17527898112

[16 -193 2336] 127 -25889931264

[8 65 544] 127 -17527898112

[2 0 64] 128 0

[2 8 96] 128 109990379520

[2 16 192] 128 0

[4 0 32] 128 0

[4 16 96] 128 -144558784512

[4 32 288] 128 0

[6 8 32] 128 109990379520

[22 -112 576] 128 144558784512

[22 -200 1824] 128 -109990379520

[22 -288 3776] 128 -144558784512

[18 -40 96] 128 -109990379520

[18 -112 704] 128 0

[18 -256 3648] 128 0

[12 16 32] 128 0

[12 -64 352] 128 144558784512

[12 -112 1056] 128 0

[68 -885 11520] 135 -211872423936

[34 -171 864] 135 -543045672960

[34 -341 3424] 135 -147205791744

[24 -267 2976] 135 19641821184

[8 11 32] 135 -211872423936

[18 -75 320] 135 -136641404928

[16 -117 864] 135 -147205791744

[12 -75 480] 135 41978161152

[72 -793 8736] 143 208833730560

[36 -217 1312] 143 -53262723072

[42 121 352] 143 145703380992

[6 7 32] 143 208833730560

[6 25 128] 143 20636608512

[18 -199 2208] 143 20636608512

[18 -217 2624] 143 -260982319104

[12 -25 64] 143 -145703380992

[14 -89 576] 143 457879738368

[14 -103 768] 143 53262723072

[76 -685 6176] 151 64592750592

[38 -77 160] 151 -26927683584

[38 -115 352] 151 -444979783680

[20 -83 352] 151 -355801737216

[8 19 64] 151 444979783680

[10 13 32] 151 -64592750592

[78 -234 704] 156 -260488790016

[78 -390 1952] 156 -260488790016

[40 -202 1024] 156 34281062400

[40 -522 6816] 156 -34281062400

[6 6 32] 156 260488790016

[26 -182 1280] 156 260488790016

[8 10 32] 156 260488790016

[20 -42 96] 156 -260488790016

[20 -182 1664] 156 -260488790016

[20 -202 2048] 156 260488790016

[10 22 64] 156 -34281062400

[82 198 480] 156 34281062400

[10 42 192] 156 190886412288

[30 -102 352] 156 -190886412288

[16 -54 192] 156 -190886412288

[16 -182 2080] 156 190886412288

[80 -561 3936] 159 190662039552

[40 -561 7872] 159 90441308160

[46 -143 448] 159 46922999808

[28 -143 736] 159 46922999808

[20 -241 2912] 159 163222640640

[30 81 224] 159 368583026688

[16 -49 160] 159 125326153728

[12 15 32] 159 190662039552

[14 -143 1472] 159 368583026688

[84 -421 2112] 167 299663542272

[42 -379 3424] 167 -253317728256

[42 -421 4224] 167 221360867328

[28 -421 6336] 167 299663542272

[36 101 288] 167 49770510336

[22 -69 224] 167 -690078922752

[22 -91 384] 167 -226212956160

[14 -155 1728] 167 690078922752

[14 -197 2784] 167 253317728256

[16 -37 96] 167 -49770510336

[88 -265 800] 175 952204019712

[44 -265 1600] 175 -416837941248

[4 9 64] 175 255882442752

[8 9 32] 175 -952204019712

[22 -265 3200] 175 -576956872704

[20 -265 3520] 175 -73367838720

[2 4 96] 176 79364751360

[90 268 800] 176 79364751360

[30 -92 288] 176 -17007771648

[30 -212 1504] 176 79364751360

[30 -332 3680] 176 17007771648

[30 -452 6816] 176 -79364751360

[22 -44 96] 176 -79364751360

[22 -132 800] 176 -79364751360

[10 12 32] 176 79364751360

[18 -92 480] 176 -17007771648

[18 -164 1504] 176 -79364751360

[18 -236 3104] 176 17007771648

[2 3 96] 183 -1057135441920

[46 -93 192] 183 134303336448

[46 -323 2272] 183 138501175296

[6 3 32] 183 -1057135441920

[24 -99 416] 183 -438981052416

[38 -125 416] 183 1327164278784

[16 -227 3232] 183 138501175296

[2 2 96] 188 -555735121920

[94 -658 4608] 188 -555735121920

[48 -146 448] 188 -192490438656

[48 -530 5856] 188 192490438656

[6 2 32] 188 -555735121920

[6 14 64] 188 192490438656

[142 350 864] 188 -192490438656

[6 50 448] 188 555735121920

[24 -146 896] 188 555735121920

[24 -338 4768] 188 -555735121920

[8 18 64] 188 192490438656

[112 274 672] 188 -192490438656

[12 14 32] 188 -555735121920

[16 -146 1344] 188 555735121920

[12 50 224] 188 -497670094848

[32 -110 384] 188 497670094848

[14 34 96] 188 192490438656

[102 242 576] 188 -192490438656

[14 62 288] 188 -497670094848

[42 -146 512] 188 497670094848

[2 1 96] 191 239856046080

[48 -673 9440] 191 527443243008

[4 33 320] 191 404325126144

[6 1 32] 191 239856046080

[32 -417 5440] 191 1065439506432

[24 -289 3488] 191 -680643219456

[8 33 160] 191 720129183744

[20 -223 2496] 191 720129183744

[36 95 256] 191 188382621696

[16 -161 1632] 191 188382621696

[18 -95 512] 191 -1065439506432

[18 -257 3680] 191 -404325126144

[2 0 96] 192 0

[2 8 128] 192 -1713289297920

[2 16 224] 192 0

[4 8 64] 192 74258055168

[52 152 448] 192 74258055168

[6 0 32] 192 0

[6 24 128] 192 -439030382592

[6 48 416] 192 0

[8 8 32] 192 -1713289297920

[24 -72 224] 192 439030382592

[24 -120 608] 192 439030382592

[24 -168 1184] 192 -1713289297920

[26 -56 128] 192 1713289297920

[26 -160 992] 192 0

[26 -368 5216] 192 0

[12 24 64] 192 74258055168

[28 72 192] 192 74258055168

[14 16 32] 192 0

[14 -72 384] 192 439030382592

[14 -128 1184] 192 0

[100 -1301 16928] 199 1438860982272

[50 -501 5024] 199 -412963817472

[50 -651 8480] 199 -1703132510208

[26 -107 448] 199 1003245520896

[26 -341 4480] 199 -1864993228800

[10 11 32] 199 1438860982272

[10 21 64] 199 -1703132510208

[16 -213 2848] 199 -1864993228800

[104 -1145 12608] 207 -33542928384

[52 -313 1888] 207 3182364672

[478 1113 2592] 207 1247150733312

[36 -327 2976] 207 -448026660864

[26 -313 3776] 207 498095425536

[26 -391 5888] 207 33542928384

[18 -39 96] 207 -448026660864

[18 -57 192] 207 470363000832

[108 -973 8768] 215 258420787200

[54 -109 224] 215 -148903704576

[54 -595 6560] 215 -81905141760

[36 -397 4384] 215 -29274617856

[6 13 64] 215 -81905141760

[28 -115 480] 215 303919577088

[42 115 320] 215 845858162688

[24 -77 256] 215 13557614592

[12 13 32] 215 -258420787200

[18 -109 672] 215 -776998238208

[20 -205 2112] 215 845858162688

[42 109 288] 215 776998238208

[16 -179 2016] 215 -13557614592

[110 -330 992] 220 -690309660672

[110 -550 2752] 220 -690309660672

[4 6 64] 220 -132152131584

[56 -506 4576] 220 132152131584

[28 -58 128] 220 -690309660672

[28 -198 1408] 220 690309660672

[28 -282 2848] 220 690309660672

[28 -422 6368] 220 -690309660672

[10 10 32] 220 690309660672

[22 -154 1088] 220 690309660672

[34 86 224] 220 -132152131584

[170 390 896] 220 132152131584

[14 58 256] 220 -87981391872

[34 -118 416] 220 87981391872

[16 -70 320] 220 87981391872

[16 -198 2464] 220 -87981391872

[112 -785 5504] 223 -1139556163584

[56 -785 11008] 223 159632449536

[4 17 128] 223 750803460096

[28 -337 4064] 223 2335794290688

[8 17 64] 223 750803460096

[14 15 32] 223 -1139556163584

[116 -581 2912] 231 -1180741177344

[4 5 64] 231 2126396559360

[58 -581 5824] 231 514227302400

[40 -123 384] 231 -1067365429248

[30 -123 512] 231 -191898021888

[30 -453 6848] 231 -1180741177344

[24 -123 640] 231 -1067365429248

[40 -133 448] 231 359044116480

[20 -123 768] 231 813571903488

[104 251 608] 231 3919640752128

[20 -187 1760] 231 813571903488

[120 -361 1088] 239 -2787471839232

[60 -361 2176] 239 -275679301632

[248 617 1536] 239 -2040942145536

[40 -361 3264] 239 2009319911424

[48 -151 480] 239 -2275766513664

[30 -151 768] 239 -2275766513664

[30 -361 4352] 239 750621143040

[24 -361 5440] 239 -2787471839232

[10 41 192] 239 2197775732736

[20 -41 96] 239 2009319911424

[198 457 1056] 239 -2040942145536

[22 -137 864] 239 -1694078717952

[22 -247 2784] 239 2197775732736

[18 -169 1600] 239 -1694078717952

[2 4 128] 240 1574084542464

[122 364 1088] 240 1574084542464

[4 4 64] 240 351561842688

[60 -180 544] 240 1574084542464

[60 -300 1504] 240 1574084542464

[60 -420 2944] 240 351561842688

[6 12 64] 240 -1574084542464

[46 132 384] 240 -1574084542464

[30 -60 128] 240 -1574084542464

[30 -180 1088] 240 -1574084542464

[8 4 32] 240 1574084542464

[32 -100 320] 240 -654995619840

[32 -228 1632] 240 1574084542464

[32 -356 3968] 240 654995619840

[10 20 64] 240 -1574084542464

[34 92 256] 240 -1574084542464

[12 12 32] 240 1574084542464

[20 -60 192] 240 -654995619840

[20 -100 512] 240 -654995619840

[20 -140 992] 240 1574084542464

[16 -36 96] 240 1574084542464

[16 -100 640] 240 -351561842688

[16 -164 1696] 240 -1574084542464

[16 -228 3264] 240 351561842688

[2 3 128] 247 2480255551488

[62 -125 256] 247 179026937856

[62 -931 13984] 247 1217370765312

[8 3 32] 247 2480255551488

[32 -131 544] 247 2297295157248

[2 2 128] 252 -487722221568

[126 -882 6176] 252 -487722221568

[4 2 64] 252 -2158506639360

[64 -450 3168] 252 -2158506639360

[42 -126 384] 252 1152280166400

[42 -210 1056] 252 1152280166400

[8 2 32] 252 -487722221568

[32 -194 1184] 252 487722221568

[32 -450 6336] 252 -487722221568

[8 66 576] 252 487722221568

[24 -126 672] 252 1152280166400

[24 -318 4224] 252 -1152280166400

[14 14 32] 252 -487722221568

[18 -126 896] 252 -487722221568

[16 -66 288] 252 -1507992109056

[16 -194 2368] 252 1507992109056

[18 -78 352] 252 -1507992109056

[18 -114 736] 252 2158506639360

[18 -222 2752] 252 1507992109056

[18 -258 3712] 252 -2158506639360

[2 1 128] 255 1018143916032

[4 1 64] 255 -2303278202880

[64 -897 12576] 255 -2386934906880

[44 -575 7520] 255 875843862528

[8 1 32] 255 1018143916032

[32 -385 4640] 255 -464085565440

[28 -257 2368] 255 -369135206400

[22 -223 2272] 255 369135206400

[22 -289 3808] 255 -2787901489152

[20 -65 224] 255 41870180352

[14 33 96] 255 875843862528

[2 0 128] 256 0

[2 8 160] 256 1062891159552

[2 16 256] 256 0

[4 0 64] 256 0

[4 16 128] 256 -299825627136

[4 32 320] 256 0

[8 0 32] 256 0

[8 16 64] 256 -299825627136

[40 112 320] 256 -299825627136

[8 32 160] 256 406906208256

[8 64 544] 256 0

[34 -72 160] 256 -1062891159552

[34 -208 1280] 256 0

[34 -480 6784] 256 0

[26 -80 256] 256 -406906208256

[26 -184 1312] 256 1062891159552

[26 -288 3200] 256 406906208256

[26 -392 5920] 256 -1062891159552

[16 16 32] 256 0

[16 -48 160] 256 -406906208256

[16 -112 800] 256 0

[20 -48 128] 256 299825627136

[20 -128 832] 256 0

[20 -288 4160] 256 0

[132 -1717 22336] 263 -5722603444224

[66 -331 1664] 263 2417410725888

[66 -661 6624] 263 -1141896960000

[44 -309 2176] 263 -864574986240

[408 949 2208] 263 2417410725888

[34 -139 576] 263 -359824533504

[34 -309 2816] 263 3737045673984

[22 -309 4352] 263 -864574986240

[22 -331 4992] 263 5722603444224

[24 -53 128] 263 3737045673984

[12 53 256] 263 -5876565878784

[18 -203 2304] 263 -5876565878784

[136 -1497 16480] 271 1186421649408

[68 -409 2464] 271 3440216911872

[74 217 640] 271 319984619520

[34 -103 320] 271 897550503936

[34 -409 4928] 271 2315619840000

[28 -423 6400] 271 -1186421649408

[134 327 800] 271 160288518144

[20 -103 544] 271 897550503936

[212 487 1120] 271 -319984619520

[124 295 704] 271 160288518144

[140 -1261 11360] 279 -75137814528

[70 -141 288] 279 -131857059840

[70 -211 640] 279 378477023232

[48 -339 2400] 279 795247902720

[36 -147 608] 279 1586228858880

[164 403 992] 279 -2082229456896

[28 -365 4768] 279 431989125120

[268 621 1440] 279 378477023232

[24 -339 4800] 279 795247902720

[42 -141 480] 279 -1277110517760

[20 -301 4544] 279 -75137814528

[98 237 576] 279 639402283008

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[40 -85 192] 455 -4275534102528

[62 -203 672] 455 7770878509056

[14 21 64] 455 -10930410356736

[30 -395 5216] 455 -746712465408

[28 -427 6528] 455 -3488393625600

[18 43 128] 455 -712762392576

[24 -341 4864] 455 8469313781760

[20 85 384] 455 -2334516707328

[24 -299 3744] 455 -2334516707328

[232 -2553 28096] 463 23084120420352

[116 -697 4192] 463 6136192413696

[1054 2457 5728] 463 49649109454848

[58 -871 13088] 463 49649109454848

[16 7 32] 463 23084120420352

[236 -2125 19136] 471 12130147289088

[118 -237 480] 471 -18864494229504

[118 -1299 14304] 471 -21938728519680

[80 -563 3968] 471 22474364663808

[74 211 608] 471 -9146011269120

[10 13 64] 471 -21938728519680

[40 -563 7936] 471 7426782345216

[12 51 256] 471 -6664586115072

[30 -333 3712] 471 -6664586115072

[24 -51 128] 471 9146011269120

[50 -173 608] 471 64765021341696

[26 -371 5312] 471 22474364663808

[26 -397 6080] 471 12130147289088

[238 -714 2144] 476 15122302304256

[238 -1190 5952] 476 15122302304256

[4 6 128] 476 -13963460542464

[120 -1082 9760] 476 13963460542464

[90 262 768] 476 26003333382144

[738 1718 4000] 476 -26003333382144

[6 26 192] 476 5576068497408

[90 -278 864] 476 -5576068497408

[60 -122 256] 476 15122302304256

[60 -422 2976] 476 -13963460542464

[60 -602 6048] 476 -15122302304256

[60 -902 13568] 476 13963460542464

[10 22 96] 476 5576068497408

[210 518 1280] 476 -5576068497408

[10 42 224] 476 -3419733295104

[62 -198 640] 476 3419733295104

[40 -122 384] 476 3419733295104

[40 -442 4896] 476 -3419733295104

[12 26 96] 476 5576068497408

[180 442 1088] 476 -5576068497408

[34 -102 320] 476 3419733295104

[34 -170 864] 476 3419733295104

[30 -122 512] 476 20930390851584

[30 -182 1120] 476 13963460542464

[30 -362 4384] 476 -20930390851584

[30 -422 5952] 476 -13963460542464

[16 6 32] 476 -15122302304256

[32 -134 576] 476 20930390851584

[32 -390 4768] 476 -20930390851584

[18 26 64] 476 -13963460542464

[30 -278 2592] 476 13963460542464

[30 -458 7008] 476 15122302304256

[24 -122 640] 476 3419733295104

[24 -314 4128] 476 -3419733295104

[48 122 320] 476 26003333382144

[248 570 1312] 476 -26003333382144

[24 -58 160] 476 -5576068497408

[24 -250 2624] 476 5576068497408

[240 -1681 11776] 479 56756228849664

[120 -1681 23552] 479 2502513917952

[4 17 192] 479 5264174481408

[80 -401 2016] 479 -13455169683456

[6 49 480] 479 -2649917030400

[8 17 96] 479 13455169683456

[48 -145 448] 479 4288417234944

[40 -401 4032] 479 -11475099156480

[54 -175 576] 479 1931542364160

[12 17 64] 479 5264174481408

[42 -593 8384] 479 6343276855296

[36 -401 4480] 479 -1931542364160

[178 433 1056] 479 -10218673668096

[28 -145 768] 479 4288417234944

[56 145 384] 479 15094673768448

[24 -145 896] 479 -15094673768448

[20 81 352] 479 -299414618112

[28 -401 5760] 479 2649917030400

[168 401 960] 479 -10218673668096

[24 -367 5632] 479 -56756228849664

[60 -209 736] 479 299414618112

[244 -1221 6112] 487 42536759924736

[4 5 128] 487 -4265407322112

[122 -1221 12224] 487 9462914684928

[62 -933 14048] 487 4265407322112

[16 5 32] 487 -42536759924736

[248 -745 2240] 495 -4349638711296

[124 -745 4480] 495 -4461404067840

[504 1257 3136] 495 -6016765421568

[6 9 96] 495 -2599177420800

[62 -311 1568] 495 -6743825836032

[52 -681 8928] 495 11034076243968

[42 -87 192] 495 -1153589575680

[36 -471 6176] 495 5236483430400

[56 151 416] 495 6375234398208

[16 23 64] 495 6016765421568

[28 -87 288] 495 -42584449247232

[142 343 832] 495 -27815009556480

[18 9 32] 495 4349638711296

[26 -265 2720] 495 6375234398208

[26 -343 4544] 495 5236483430400

[28 -151 832] 495 -11034076243968

[24 -105 480] 495 7899666186240

[2 4 256] 496 -33473389658112

[250 748 2240] 496 -33473389658112

[4 4 128] 496 8890598031360

[124 -372 1120] 496 19595746344960

[124 -620 3104] 496 19595746344960

[124 -868 6080] 496 8890598031360

[62 -124 256] 496 33473389658112

[62 -372 2240] 496 33473389658112

[8 4 64] 496 8890598031360

[64 -196 608] 496 -5718103031808

[64 -452 3200] 496 8890598031360

[64 -708 7840] 496 5718103031808

[10 12 64] 496 -19595746344960

[50 -252 1280] 496 -5718103031808

[50 -452 4096] 496 19595746344960

[50 -652 8512] 496 5718103031808

[14 20 64] 496 -19595746344960

[38 -196 1024] 496 -5718103031808

[38 -348 3200] 496 19595746344960

[38 -500 6592] 496 5718103031808

[16 4 32] 496 -33473389658112

[32 -68 160] 496 19595746344960

[32 -196 1216] 496 -8890598031360

[32 -324 3296] 496 -19595746344960

[32 -452 6400] 496 8890598031360

[16 68 320] 496 12424257208320

[56 -188 640] 496 -12424257208320

[20 28 64] 496 8890598031360

[28 -92 320] 496 -12424257208320

[28 -148 800] 496 -5718103031808

[28 -260 2432] 496 -8890598031360

[28 -316 3584] 496 12424257208320

[28 -372 4960] 496 5718103031808

[28 -428 6560] 496 33473389658112

A nonlift newform in S9(K(16))−

A nonlift newform in S₉(K(16))⁻