Space of modular forms of level 1156 and weight 1

• Label: 1156.1
• Level: 1156
• Weight: 1
• Dimension: 85
• Nonzero newspaces: 7
• Newform subspaces: 10
• Sturm bound: 83232
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(83232\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1156))\).

	Total	New	Old
Modular forms	1091	454	637
Cusp forms	91	85	6
Eisenstein series	1000	369	631

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	85	0	0	0

Trace form

\( 85 q + q^{2} + q^{4} + 2 q^{5} + q^{8} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1156))\)

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
1156.1.c	\(\chi_{1156}(579, \cdot)\)	1156.1.c.a	1	1
		1156.1.c.b	2
1156.1.d	\(\chi_{1156}(1155, \cdot)\)	1156.1.d.a	2	1
1156.1.f	\(\chi_{1156}(251, \cdot)\)	1156.1.f.a	2	2
		1156.1.f.b	2
1156.1.g	\(\chi_{1156}(155, \cdot)\)	1156.1.g.a	4	4
		1156.1.g.b	8
1156.1.j	\(\chi_{1156}(65, \cdot)\)	None	0	8
1156.1.l	\(\chi_{1156}(67, \cdot)\)	1156.1.l.a	16	16
1156.1.m	\(\chi_{1156}(35, \cdot)\)	1156.1.m.a	16	16
1156.1.o	\(\chi_{1156}(47, \cdot)\)	1156.1.o.a	32	32
1156.1.r	\(\chi_{1156}(15, \cdot)\)	None	0	64
1156.1.s	\(\chi_{1156}(5, \cdot)\)	None	0	128

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1156))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1156)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)