Space of modular forms of level 308 and weight 4

• Label: 308.4
• Level: 308
• Weight: 4
• Dimension: 4658
• Nonzero newspaces: 16
• Sturm bound: 23040
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(23040\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(308))\).

	Total	New	Old
Modular forms	8940	4834	4106
Cusp forms	8340	4658	3682
Eisenstein series	600	176	424

Trace form

4658 * q - 14 * q^2 + 12 * q^3 - 14 * q^4 - 52 * q^5 - 20 * q^6 - 38 * q^7 - 140 * q^8 - 272 * q^9 - 6 * q^10 - 16 * q^11 + 296 * q^12 + 220 * q^13 + 118 * q^14 + 164 * q^15 - 206 * q^16 + 180 * q^17 + 388 * q^18 - 186 * q^19 + 930 * q^20 - 924 * q^21 + 1084 * q^22 + 792 * q^23 + 184 * q^24 + 1904 * q^25 - 762 * q^26 + 894 * q^27 - 1840 * q^28 + 400 * q^29 - 3590 * q^30 - 2652 * q^31 - 1704 * q^32 - 4550 * q^33 + 1840 * q^34 - 1936 * q^35 + 2742 * q^36 - 1280 * q^37 + 2570 * q^38 + 2228 * q^39 + 906 * q^40 + 5540 * q^41 + 1688 * q^42 + 4868 * q^43 - 948 * q^44 + 10008 * q^45 - 374 * q^46 + 1256 * q^47 - 2550 * q^48 - 956 * q^49 - 4268 * q^50 - 5162 * q^51 - 8434 * q^52 - 11256 * q^53 - 9174 * q^54 - 7612 * q^55 - 6114 * q^56 - 10182 * q^57 - 2658 * q^58 - 1150 * q^59 + 1714 * q^60 - 1460 * q^61 + 7930 * q^62 - 3244 * q^63 + 11044 * q^64 + 2812 * q^65 + 12702 * q^66 + 8884 * q^67 + 19818 * q^68 + 7844 * q^69 + 19078 * q^70 + 5472 * q^71 + 23062 * q^72 + 8036 * q^73 + 7578 * q^74 + 13726 * q^75 + 6392 * q^77 - 16088 * q^78 + 1704 * q^79 - 29094 * q^80 + 6074 * q^81 - 29384 * q^82 + 230 * q^83 - 27896 * q^84 - 2156 * q^85 - 21440 * q^86 - 764 * q^87 - 17510 * q^88 + 5156 * q^89 - 20190 * q^90 - 9620 * q^91 - 9168 * q^92 - 15068 * q^93 - 1030 * q^94 - 14392 * q^95 + 12098 * q^96 - 9490 * q^97 + 19488 * q^98 - 5792 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(308))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
308.4.a	\(\chi_{308}(1, \cdot)\)	308.4.a.a	1	1
		308.4.a.b	1
		308.4.a.c	3
		308.4.a.d	4
		308.4.a.e	5
308.4.c	\(\chi_{308}(153, \cdot)\)	308.4.c.a	24	1
308.4.d	\(\chi_{308}(43, \cdot)\)	n/a	108	1
308.4.f	\(\chi_{308}(111, \cdot)\)	n/a	120	1
308.4.i	\(\chi_{308}(177, \cdot)\)	308.4.i.a	20	2
		308.4.i.b	20
308.4.j	\(\chi_{308}(113, \cdot)\)	308.4.j.a	36	4
		308.4.j.b	36
308.4.l	\(\chi_{308}(199, \cdot)\)	n/a	240	2
308.4.n	\(\chi_{308}(219, \cdot)\)	n/a	280	2
308.4.q	\(\chi_{308}(241, \cdot)\)	308.4.q.a	48	2
308.4.t	\(\chi_{308}(27, \cdot)\)	n/a	560	4
308.4.v	\(\chi_{308}(127, \cdot)\)	n/a	432	4
308.4.w	\(\chi_{308}(13, \cdot)\)	308.4.w.a	96	4
308.4.y	\(\chi_{308}(9, \cdot)\)	n/a	192	8
308.4.z	\(\chi_{308}(17, \cdot)\)	n/a	192	8
308.4.bc	\(\chi_{308}(39, \cdot)\)	n/a	1120	8
308.4.be	\(\chi_{308}(3, \cdot)\)	n/a	1120	8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(308))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(308)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 1}\)