Space of modular forms of level 304 and weight 2

• Label: 304.2
• Level: 304
• Weight: 2
• Dimension: 1535
• Nonzero newspaces: 12
• Newform subspaces: 40
• Sturm bound: 11520
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 40 \)
Sturm bound:			\(11520\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(304))\).

	Total	New	Old
Modular forms	3132	1687	1445
Cusp forms	2629	1535	1094
Eisenstein series	503	152	351

Trace form

1535 * q - 32 * q^2 - 23 * q^3 - 36 * q^4 - 41 * q^5 - 44 * q^6 - 27 * q^7 - 44 * q^8 - 9 * q^9 - 36 * q^10 - 31 * q^11 - 28 * q^12 - 41 * q^13 - 28 * q^14 - 35 * q^15 - 20 * q^16 - 73 * q^17 - 40 * q^18 - 33 * q^19 - 80 * q^20 - 53 * q^21 - 36 * q^22 - 27 * q^23 - 36 * q^24 - 9 * q^25 - 44 * q^26 - 11 * q^27 - 52 * q^28 - 57 * q^29 - 28 * q^30 + 5 * q^31 - 52 * q^32 - 73 * q^33 - 44 * q^34 - 19 * q^35 - 28 * q^36 - 66 * q^37 - 24 * q^38 - 54 * q^39 - 20 * q^40 - 9 * q^41 - 36 * q^42 - 47 * q^43 - 28 * q^44 - 49 * q^45 - 60 * q^46 - 59 * q^47 - 52 * q^48 - 93 * q^49 - 24 * q^50 - 35 * q^51 - 28 * q^52 - 25 * q^53 - 36 * q^54 - 27 * q^55 - 20 * q^56 - 9 * q^57 - 48 * q^58 - 15 * q^59 - 36 * q^60 - 45 * q^61 - 68 * q^62 - 107 * q^63 - 36 * q^64 - 161 * q^65 - 44 * q^66 - 115 * q^67 - 36 * q^68 - 93 * q^69 - 52 * q^70 - 81 * q^71 - 44 * q^72 - 117 * q^73 - 36 * q^74 - 156 * q^75 - 48 * q^76 - 206 * q^77 - 28 * q^78 - 153 * q^79 - 52 * q^80 - 209 * q^81 - 36 * q^82 - 77 * q^83 - 20 * q^84 - 125 * q^85 - 36 * q^86 - 135 * q^87 - 52 * q^88 - 81 * q^89 - 28 * q^90 - 107 * q^91 + 12 * q^92 - 113 * q^93 - 4 * q^94 - 15 * q^95 - 40 * q^96 - 73 * q^97 - 24 * q^98 - 23 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)

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
304.2.a	\(\chi_{304}(1, \cdot)\)	304.2.a.a	1	1
		304.2.a.b	1
		304.2.a.c	1
		304.2.a.d	1
		304.2.a.e	1
		304.2.a.f	1
		304.2.a.g	3
304.2.b	\(\chi_{304}(151, \cdot)\)	None	0	1
304.2.c	\(\chi_{304}(153, \cdot)\)	None	0	1
304.2.h	\(\chi_{304}(303, \cdot)\)	304.2.h.a	2	1
		304.2.h.b	4
		304.2.h.c	4
304.2.i	\(\chi_{304}(49, \cdot)\)	304.2.i.a	2	2
		304.2.i.b	2
		304.2.i.c	2
		304.2.i.d	2
		304.2.i.e	4
		304.2.i.f	6
304.2.k	\(\chi_{304}(77, \cdot)\)	304.2.k.a	4	2
		304.2.k.b	68
304.2.m	\(\chi_{304}(75, \cdot)\)	304.2.m.a	76	2
304.2.n	\(\chi_{304}(31, \cdot)\)	304.2.n.a	2	2
		304.2.n.b	2
		304.2.n.c	4
		304.2.n.d	6
		304.2.n.e	6
304.2.s	\(\chi_{304}(103, \cdot)\)	None	0	2
304.2.t	\(\chi_{304}(121, \cdot)\)	None	0	2
304.2.u	\(\chi_{304}(17, \cdot)\)	304.2.u.a	6	6
		304.2.u.b	6
		304.2.u.c	6
		304.2.u.d	6
		304.2.u.e	12
		304.2.u.f	18
304.2.v	\(\chi_{304}(45, \cdot)\)	304.2.v.a	152	4
304.2.x	\(\chi_{304}(27, \cdot)\)	304.2.x.a	4	4
		304.2.x.b	4
		304.2.x.c	144
304.2.bb	\(\chi_{304}(9, \cdot)\)	None	0	6
304.2.bd	\(\chi_{304}(71, \cdot)\)	None	0	6
304.2.be	\(\chi_{304}(15, \cdot)\)	304.2.be.a	12	6
		304.2.be.b	12
		304.2.be.c	18
		304.2.be.d	18
304.2.bg	\(\chi_{304}(3, \cdot)\)	304.2.bg.a	456	12
304.2.bi	\(\chi_{304}(5, \cdot)\)	304.2.bi.a	456	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(304)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 1}\)