Space of modular forms of level 131 and weight 1

• Label: 131.1
• Level: 131
• Weight: 1
• Dimension: 2
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 1430
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 131 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1430\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(131))\).

	Total	New	Old
Modular forms	67	67	0
Cusp forms	2	2	0
Eisenstein series	65	65	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

2 * q - q^3 + 2 * q^4 - q^5 - q^7 + q^9 - q^11 - q^12 - q^13 - 2 * q^15 + 2 * q^16 - q^20 - 2 * q^21 + q^25 - 2 * q^27 - q^28 + 3 * q^33 + 3 * q^35 + q^36 + 3 * q^39 - q^41 - q^43 - q^44 + 2 * q^45 - q^48 + q^49 - q^52 + 4 * q^53 - 2 * q^55 - q^59 - 2 * q^60 - q^61 + 2 * q^63 + 2 * q^64 - 2 * q^65 + 2 * q^75 - 2 * q^77 - q^80 - 2 * q^84 + 4 * q^89 - 2 * q^91 - 3 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(131))\)

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
131.1.b	\(\chi_{131}(130, \cdot)\)	131.1.b.a	2	1
131.1.d	\(\chi_{131}(42, \cdot)\)	None	0	4
131.1.f	\(\chi_{131}(18, \cdot)\)	None	0	12
131.1.h	\(\chi_{131}(2, \cdot)\)	None	0	48