Space of modular forms of level 920 and weight 1

• Label: 920.1
• Level: 920
• Weight: 1
• Dimension: 32
• Nonzero newspaces: 2
• Newform subspaces: 7
• Sturm bound: 50688
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(50688\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(920))\).

	Total	New	Old
Modular forms	1146	284	862
Cusp forms	90	32	58
Eisenstein series	1056	252	804

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

32 * q + 2 * q^4 - 4 * q^6 - 2 * q^9 - 2 * q^10 - 4 * q^11 - 4 * q^14 + 10 * q^16 - 4 * q^19 - 4 * q^24 + 6 * q^25 - 8 * q^26 - 4 * q^31 + 18 * q^35 + 6 * q^36 - 8 * q^39 - 2 * q^40 - 8 * q^41 - 4 * q^44 - 6 * q^46 - 6 * q^49 + 4 * q^50 - 8 * q^54 - 4 * q^56 + 18 * q^59 + 2 * q^64 - 4 * q^65 - 4 * q^70 - 12 * q^71 - 4 * q^74 - 4 * q^76 + 2 * q^81 - 4 * q^89 - 2 * q^90 - 8 * q^91 - 4 * q^94 - 4 * q^96 - 4 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(920))\)

We only show spaces with odd 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
920.1.c	\(\chi_{920}(231, \cdot)\)	None	0	1
920.1.d	\(\chi_{920}(781, \cdot)\)	None	0	1
920.1.g	\(\chi_{920}(689, \cdot)\)	None	0	1
920.1.h	\(\chi_{920}(139, \cdot)\)	None	0	1
920.1.k	\(\chi_{920}(321, \cdot)\)	None	0	1
920.1.l	\(\chi_{920}(691, \cdot)\)	None	0	1
920.1.o	\(\chi_{920}(599, \cdot)\)	None	0	1
920.1.p	\(\chi_{920}(229, \cdot)\)	920.1.p.a	2	1
		920.1.p.b	2
		920.1.p.c	2
		920.1.p.d	2
		920.1.p.e	4
920.1.r	\(\chi_{920}(93, \cdot)\)	None	0	2
920.1.t	\(\chi_{920}(643, \cdot)\)	None	0	2
920.1.u	\(\chi_{920}(183, \cdot)\)	None	0	2
920.1.w	\(\chi_{920}(553, \cdot)\)	None	0	2
920.1.z	\(\chi_{920}(109, \cdot)\)	None	0	10
920.1.ba	\(\chi_{920}(39, \cdot)\)	None	0	10
920.1.bd	\(\chi_{920}(131, \cdot)\)	None	0	10
920.1.be	\(\chi_{920}(201, \cdot)\)	None	0	10
920.1.bh	\(\chi_{920}(59, \cdot)\)	920.1.bh.a	10	10
		920.1.bh.b	10
920.1.bi	\(\chi_{920}(89, \cdot)\)	None	0	10
920.1.bl	\(\chi_{920}(21, \cdot)\)	None	0	10
920.1.bm	\(\chi_{920}(31, \cdot)\)	None	0	10
920.1.bp	\(\chi_{920}(73, \cdot)\)	None	0	20
920.1.br	\(\chi_{920}(7, \cdot)\)	None	0	20
920.1.bs	\(\chi_{920}(43, \cdot)\)	None	0	20
920.1.bu	\(\chi_{920}(13, \cdot)\)	None	0	20

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(920))\) into lower level spaces

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