Space of modular forms of level 1175 and weight 1

• Label: 1175.1
• Level: 1175
• Weight: 1
• Dimension: 26
• Nonzero newspaces: 2
• Newform subspaces: 8
• Sturm bound: 110400
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(110400\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1175))\).

	Total	New	Old
Modular forms	1320	949	371
Cusp forms	32	26	6
Eisenstein series	1288	923	365

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	26	0	0	0

Trace form

\( 26 q + q^{2} + q^{3} - q^{4} - 6 q^{6} + q^{7} + 2 q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1175))\)

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
1175.1.b	\(\chi_{1175}(1174, \cdot)\)	1175.1.b.a	2	1
		1175.1.b.b	4
		1175.1.b.c	8
1175.1.d	\(\chi_{1175}(751, \cdot)\)	1175.1.d.a	1	1
		1175.1.d.b	1
		1175.1.d.c	2
		1175.1.d.d	4
		1175.1.d.e	4
1175.1.f	\(\chi_{1175}(518, \cdot)\)	None	0	2
1175.1.h	\(\chi_{1175}(46, \cdot)\)	None	0	4
1175.1.j	\(\chi_{1175}(234, \cdot)\)	None	0	4
1175.1.k	\(\chi_{1175}(48, \cdot)\)	None	0	8
1175.1.n	\(\chi_{1175}(26, \cdot)\)	None	0	22
1175.1.p	\(\chi_{1175}(99, \cdot)\)	None	0	22
1175.1.q	\(\chi_{1175}(7, \cdot)\)	None	0	44
1175.1.t	\(\chi_{1175}(19, \cdot)\)	None	0	88
1175.1.v	\(\chi_{1175}(11, \cdot)\)	None	0	88
1175.1.x	\(\chi_{1175}(2, \cdot)\)	None	0	176

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1175))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1175)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 3}\)