Spanning S_k(K(4))^± and S_k(K(8))^± and nonlift newform eigenvalues

Click on a nonzero nonlift dimension to see how the Fricke eigenspace was spanned.

S_k(K(4))

k	dim S_k(K(4))	Lifts	Plus Nonlifts	3^k−3λ₃ for plus nonlift newforms	Minus Nonlifts	3^k−3λ₃ for minus nonlift newforms
1	0	0	0		0
2	0	0	0		0
3	0	0	0		0
4	0	0	0		0
5	0	0	0		0
6	0	0	0		0
7	1	1 (−)	0		0
8	1	1 (+)	0		0
9	1	1 (−)	0		0
10	2	2 (+)	0		0
11	3	2 (−)	0		1	-13464
12	4	3 (+)	1	-88488	0
13	3	2 (−)	0		1	-15440
14	5	3 (+)	2	-1422360 -319896	0

S_k(K(8))

k	dim S_k(K(8))	Lifts	Plus Nonlifts	3^k−3λ₃ for plus nonlift newforms	Minus Nonlifts	3^k−3λ₃ for minus nonlift newforms
1	0	0	0		0
2	0	0	0		0
3	0	0	0		0
4	0	0	0		0
5	1	1 (−)	0		0
6	1	1 (+)	0		0
7	2	2 (−)	0		0
8	3	3 (+)	0		0
9	4	3 (−)	0		1	-2760
10	6	4 (+)	2	-18360 -3672	0
11	9	5 (−)	1		3	-18744±3072√55
12	12	6 (+)	5	-14760 -229032 504(65±64√6)	1
13	13	5 (−)	2	-685524	6	-271944 α_13,8 (degree 4)
14	19	7 (+)	9	199368 -1176984 265896±1728√1129 α_14,8 (degree 3)	3	-1580472

Definition of algebraic numbers in the table.

α_13,8 is a root of x^4+463392x^3+271045699200x^2 -28599118413428736x +151059326544225331200
α_14,8 is a root of x^3+186408x^2 -1194997748544x +70155550286581248