Properties

Label 961.1
Level 961
Weight 1
Dimension 14
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 76880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 961 = 31^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(76880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(961))\).

Total New Old
Modular forms 706 674 32
Cusp forms 16 14 2
Eisenstein series 690 660 30

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14 q + q^{2} + q^{5} + q^{7} - q^{8} - q^{9} + O(q^{10}) \) \( 14 q + q^{2} + q^{5} + q^{7} - q^{8} - q^{9} - q^{10} - q^{14} + q^{16} + q^{18} + q^{19} - q^{35} - q^{38} + q^{40} + q^{41} + q^{45} - 2 q^{47} + q^{56} + q^{59} - 14 q^{63} - q^{64} - 2 q^{67} + q^{70} + q^{71} - q^{72} - q^{80} - q^{81} - q^{82} - q^{90} - 28 q^{94} - q^{95} + q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(961))\)

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
961.1.b \(\chi_{961}(960, \cdot)\) None 0 1
961.1.e \(\chi_{961}(440, \cdot)\) 961.1.e.a 2 2
961.1.f \(\chi_{961}(333, \cdot)\) 961.1.f.a 4 4
961.1.h \(\chi_{961}(115, \cdot)\) 961.1.h.a 8 8
961.1.j \(\chi_{961}(30, \cdot)\) None 0 30
961.1.m \(\chi_{961}(6, \cdot)\) None 0 60
961.1.n \(\chi_{961}(15, \cdot)\) None 0 120
961.1.p \(\chi_{961}(3, \cdot)\) None 0 240

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(961))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(961)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(961))\)\(^{\oplus 1}\)