Space of modular forms of level 476 and weight 2

• Label: 476.2
• Level: 476
• Weight: 2
• Dimension: 3688
• Nonzero newspaces: 20
• Newform subspaces: 30
• Sturm bound: 27648
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 30 \)
Sturm bound:			\(27648\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(476))\).

	Total	New	Old
Modular forms	7392	3984	3408
Cusp forms	6433	3688	2745
Eisenstein series	959	296	663

Trace form

3688 * q - 26 * q^2 + 2 * q^3 - 26 * q^4 - 46 * q^5 - 32 * q^6 + 8 * q^7 - 74 * q^8 - 56 * q^9 - 44 * q^10 + 10 * q^11 - 56 * q^12 - 56 * q^13 - 58 * q^14 + 36 * q^15 - 66 * q^16 - 39 * q^17 - 70 * q^18 + 14 * q^19 - 32 * q^20 - 66 * q^21 - 44 * q^22 + 22 * q^23 - 40 * q^24 - 92 * q^25 - 72 * q^26 - 28 * q^27 - 34 * q^28 - 200 * q^29 - 148 * q^30 - 78 * q^31 - 106 * q^32 - 178 * q^33 - 160 * q^34 - 62 * q^35 - 226 * q^36 - 142 * q^37 - 148 * q^38 - 28 * q^39 - 184 * q^40 - 80 * q^41 - 112 * q^42 - 132 * q^44 - 52 * q^45 - 88 * q^46 + 62 * q^47 + 16 * q^48 - 16 * q^49 - 102 * q^50 + 67 * q^51 - 64 * q^52 + 18 * q^53 + 36 * q^54 + 68 * q^55 - 18 * q^56 - 180 * q^57 + 92 * q^58 + 50 * q^59 + 200 * q^60 - 94 * q^61 + 80 * q^62 - 4 * q^63 - 2 * q^64 - 260 * q^65 + 156 * q^66 - 46 * q^67 + 144 * q^68 - 300 * q^69 + 20 * q^70 + 206 * q^72 - 262 * q^73 + 88 * q^74 - 24 * q^75 + 80 * q^76 - 138 * q^77 + 80 * q^78 + 6 * q^79 + 48 * q^80 - 214 * q^81 + 24 * q^82 - 48 * q^83 - 48 * q^84 - 182 * q^85 - 188 * q^86 - 12 * q^87 - 196 * q^88 - 190 * q^89 - 192 * q^90 - 292 * q^92 - 154 * q^93 - 164 * q^94 - 102 * q^95 - 288 * q^96 - 24 * q^97 - 146 * q^98 - 152 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)

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
476.2.a	\(\chi_{476}(1, \cdot)\)	476.2.a.a	2	1
		476.2.a.b	2
		476.2.a.c	2
		476.2.a.d	2
476.2.b	\(\chi_{476}(169, \cdot)\)	476.2.b.a	8	1
476.2.e	\(\chi_{476}(475, \cdot)\)	476.2.e.a	8	1
		476.2.e.b	20
		476.2.e.c	40
476.2.f	\(\chi_{476}(307, \cdot)\)	476.2.f.a	64	1
476.2.i	\(\chi_{476}(137, \cdot)\)	476.2.i.a	2	2
		476.2.i.b	2
		476.2.i.c	2
		476.2.i.d	6
		476.2.i.e	8
476.2.k	\(\chi_{476}(55, \cdot)\)	476.2.k.a	136	2
476.2.l	\(\chi_{476}(225, \cdot)\)	476.2.l.a	16	2
476.2.p	\(\chi_{476}(103, \cdot)\)	476.2.p.a	128	2
476.2.q	\(\chi_{476}(271, \cdot)\)	476.2.q.a	16	2
		476.2.q.b	120
476.2.t	\(\chi_{476}(305, \cdot)\)	476.2.t.a	24	2
476.2.u	\(\chi_{476}(253, \cdot)\)	476.2.u.a	40	4
476.2.w	\(\chi_{476}(83, \cdot)\)	476.2.w.a	272	4
476.2.z	\(\chi_{476}(47, \cdot)\)	476.2.z.a	272	4
476.2.ba	\(\chi_{476}(81, \cdot)\)	476.2.ba.a	48	4
476.2.bd	\(\chi_{476}(71, \cdot)\)	476.2.bd.a	432	8
476.2.be	\(\chi_{476}(41, \cdot)\)	476.2.be.a	96	8
476.2.bh	\(\chi_{476}(9, \cdot)\)	476.2.bh.a	96	8
476.2.bj	\(\chi_{476}(19, \cdot)\)	476.2.bj.a	544	8
476.2.bl	\(\chi_{476}(5, \cdot)\)	476.2.bl.a	192	16
476.2.bm	\(\chi_{476}(11, \cdot)\)	476.2.bm.a	1088	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(476))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(476)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 2}\)