Space of modular forms of level 308 and weight 2

• Label: 308.2
• Level: 308
• Weight: 2
• Dimension: 1494
• Nonzero newspaces: 16
• Newform subspaces: 29
• Sturm bound: 11520
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 29 \)
Sturm bound:			\(11520\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(308))\).

	Total	New	Old
Modular forms	3180	1670	1510
Cusp forms	2581	1494	1087
Eisenstein series	599	176	423

Trace form

1494 * q - 14 * q^2 + 2 * q^3 - 14 * q^4 - 22 * q^5 - 20 * q^6 + 13 * q^7 - 44 * q^8 - 12 * q^9 - 42 * q^10 + 7 * q^11 - 64 * q^12 - 38 * q^13 - 48 * q^14 - 12 * q^15 - 78 * q^16 - 32 * q^17 - 76 * q^18 - 32 * q^19 - 70 * q^20 - 90 * q^21 - 92 * q^22 - 4 * q^23 - 56 * q^24 - 64 * q^25 - 46 * q^26 + 20 * q^27 + 4 * q^28 - 90 * q^29 - 18 * q^30 - 14 * q^31 - 24 * q^32 - 29 * q^33 - 15 * q^35 - 18 * q^36 - 114 * q^37 - 6 * q^38 - 6 * q^39 + 26 * q^40 - 94 * q^41 - 4 * q^42 + 36 * q^43 + 32 * q^44 - 192 * q^45 + 6 * q^46 - 8 * q^47 + 90 * q^48 - 23 * q^49 - 36 * q^50 - 4 * q^51 - 10 * q^52 - 88 * q^53 + 6 * q^54 - 2 * q^55 - 98 * q^56 - 94 * q^57 - 78 * q^58 - 22 * q^59 - 86 * q^60 - 26 * q^61 - 170 * q^62 - 70 * q^63 - 188 * q^64 - 182 * q^65 - 144 * q^66 - 104 * q^67 - 150 * q^68 - 272 * q^69 - 62 * q^70 - 160 * q^71 - 90 * q^72 - 182 * q^73 - 86 * q^74 - 222 * q^75 - 176 * q^77 - 128 * q^78 - 126 * q^79 + 58 * q^80 - 260 * q^81 + 16 * q^82 - 88 * q^83 - 20 * q^84 - 150 * q^85 + 116 * q^86 - 62 * q^87 + 122 * q^88 - 128 * q^89 + 70 * q^90 - 39 * q^91 - 48 * q^92 - 96 * q^93 + 90 * q^94 + 14 * q^95 + 18 * q^96 + 20 * q^97 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)

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
308.2.a	\(\chi_{308}(1, \cdot)\)	308.2.a.a	1	1
		308.2.a.b	2
		308.2.a.c	3
308.2.c	\(\chi_{308}(153, \cdot)\)	308.2.c.a	4	1
		308.2.c.b	4
308.2.d	\(\chi_{308}(43, \cdot)\)	308.2.d.a	18	1
		308.2.d.b	18
308.2.f	\(\chi_{308}(111, \cdot)\)	308.2.f.a	40	1
308.2.i	\(\chi_{308}(177, \cdot)\)	308.2.i.a	6	2
		308.2.i.b	6
308.2.j	\(\chi_{308}(113, \cdot)\)	308.2.j.a	4	4
		308.2.j.b	8
		308.2.j.c	12
308.2.l	\(\chi_{308}(199, \cdot)\)	308.2.l.a	80	2
308.2.n	\(\chi_{308}(219, \cdot)\)	308.2.n.a	4	2
		308.2.n.b	4
		308.2.n.c	80
308.2.q	\(\chi_{308}(241, \cdot)\)	308.2.q.a	16	2
308.2.t	\(\chi_{308}(27, \cdot)\)	308.2.t.a	8	4
		308.2.t.b	8
		308.2.t.c	160
308.2.v	\(\chi_{308}(127, \cdot)\)	308.2.v.a	72	4
		308.2.v.b	72
308.2.w	\(\chi_{308}(13, \cdot)\)	308.2.w.a	32	4
308.2.y	\(\chi_{308}(9, \cdot)\)	308.2.y.a	16	8
		308.2.y.b	48
308.2.z	\(\chi_{308}(17, \cdot)\)	308.2.z.a	64	8
308.2.bc	\(\chi_{308}(39, \cdot)\)	308.2.bc.a	352	8
308.2.be	\(\chi_{308}(3, \cdot)\)	308.2.be.a	352	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(308))\) into lower level spaces

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