Space of modular forms of level 920 and weight 2

• Label: 920.2
• Level: 920
• Weight: 2
• Dimension: 12766
• Nonzero newspaces: 18
• Newform subspaces: 41
• Sturm bound: 101376
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 41 \)
Sturm bound:			\(101376\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(920))\).

	Total	New	Old
Modular forms	26400	13270	13130
Cusp forms	24289	12766	11523
Eisenstein series	2111	504	1607

Trace form

12766 * q - 36 * q^2 - 36 * q^3 - 36 * q^4 + 2 * q^5 - 116 * q^6 - 28 * q^7 - 36 * q^8 - 62 * q^9 - 58 * q^10 - 108 * q^11 - 60 * q^12 + 4 * q^13 - 60 * q^14 - 74 * q^15 - 148 * q^16 - 76 * q^17 - 92 * q^18 - 68 * q^19 - 98 * q^20 - 16 * q^21 - 76 * q^22 - 44 * q^23 - 136 * q^24 - 106 * q^25 - 148 * q^26 - 60 * q^27 - 28 * q^28 + 12 * q^29 - 66 * q^30 - 132 * q^31 + 4 * q^32 - 72 * q^33 + 28 * q^34 - 60 * q^35 - 52 * q^36 + 76 * q^37 + 4 * q^38 + 28 * q^39 + 22 * q^40 - 184 * q^41 + 4 * q^42 + 4 * q^43 - 12 * q^44 + 68 * q^45 - 100 * q^46 - 48 * q^47 - 28 * q^48 + 30 * q^49 - 98 * q^50 - 60 * q^51 - 84 * q^52 + 32 * q^53 - 92 * q^54 - 78 * q^55 - 228 * q^56 - 32 * q^57 - 132 * q^58 - 40 * q^59 - 146 * q^60 + 44 * q^61 - 156 * q^62 - 28 * q^63 - 108 * q^64 - 160 * q^65 - 296 * q^66 - 4 * q^67 - 84 * q^68 - 8 * q^69 - 132 * q^70 - 84 * q^71 - 20 * q^72 - 140 * q^73 - 48 * q^74 + 20 * q^75 - 352 * q^76 + 32 * q^77 - 356 * q^78 - 16 * q^79 - 216 * q^80 - 534 * q^81 - 236 * q^82 - 56 * q^83 - 596 * q^84 - 70 * q^85 - 588 * q^86 - 344 * q^87 - 396 * q^88 - 248 * q^89 - 476 * q^90 - 408 * q^91 - 424 * q^92 - 504 * q^94 - 174 * q^95 - 1064 * q^96 - 192 * q^97 - 420 * q^98 - 432 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(920))\)

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
920.2.a	\(\chi_{920}(1, \cdot)\)	920.2.a.a	1	1
		920.2.a.b	1
		920.2.a.c	1
		920.2.a.d	1
		920.2.a.e	2
		920.2.a.f	2
		920.2.a.g	3
		920.2.a.h	3
		920.2.a.i	3
		920.2.a.j	5
920.2.b	\(\chi_{920}(459, \cdot)\)	920.2.b.a	4	1
		920.2.b.b	136
920.2.e	\(\chi_{920}(369, \cdot)\)	920.2.e.a	2	1
		920.2.e.b	14
		920.2.e.c	16
920.2.f	\(\chi_{920}(461, \cdot)\)	920.2.f.a	2	1
		920.2.f.b	8
		920.2.f.c	30
		920.2.f.d	48
920.2.i	\(\chi_{920}(551, \cdot)\)	None	0	1
920.2.j	\(\chi_{920}(829, \cdot)\)	920.2.j.a	132	1
920.2.m	\(\chi_{920}(919, \cdot)\)	None	0	1
920.2.n	\(\chi_{920}(91, \cdot)\)	920.2.n.a	48	1
		920.2.n.b	48
920.2.q	\(\chi_{920}(137, \cdot)\)	920.2.q.a	72	2
920.2.s	\(\chi_{920}(47, \cdot)\)	None	0	2
920.2.v	\(\chi_{920}(323, \cdot)\)	920.2.v.a	264	2
920.2.x	\(\chi_{920}(413, \cdot)\)	920.2.x.a	8	2
		920.2.x.b	8
		920.2.x.c	264
920.2.y	\(\chi_{920}(41, \cdot)\)	920.2.y.a	50	10
		920.2.y.b	60
		920.2.y.c	60
		920.2.y.d	70
920.2.bb	\(\chi_{920}(11, \cdot)\)	920.2.bb.a	480	10
		920.2.bb.b	480
920.2.bc	\(\chi_{920}(79, \cdot)\)	None	0	10
920.2.bf	\(\chi_{920}(29, \cdot)\)	920.2.bf.a	1400	10
920.2.bg	\(\chi_{920}(111, \cdot)\)	None	0	10
920.2.bj	\(\chi_{920}(101, \cdot)\)	920.2.bj.a	960	10
920.2.bk	\(\chi_{920}(9, \cdot)\)	920.2.bk.a	360	10
920.2.bn	\(\chi_{920}(19, \cdot)\)	920.2.bn.a	40	10
		920.2.bn.b	1360
920.2.bo	\(\chi_{920}(37, \cdot)\)	920.2.bo.a	2800	20
920.2.bq	\(\chi_{920}(3, \cdot)\)	920.2.bq.a	2800	20
920.2.bt	\(\chi_{920}(87, \cdot)\)	None	0	20
920.2.bv	\(\chi_{920}(17, \cdot)\)	920.2.bv.a	720	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 2}\)