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Properties

Label 116.1
Level 116
Weight 1
Dimension 8
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 116 = 2^{2} \cdot 29 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(116))\).

Total New Old
Modular forms 78 34 44
Cusp forms 8 8 0
Eisenstein series 70 26 44

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - q^{2} + q^{4} - 4 q^{5} - 2 q^{6} - q^{8} - q^{9} + O(q^{10}) \) \( 8 q - q^{2} + q^{4} - 4 q^{5} - 2 q^{6} - q^{8} - q^{9} - 2 q^{10} - 4 q^{13} + q^{16} - 2 q^{17} - q^{18} + 3 q^{20} - 2 q^{22} - 2 q^{24} - 3 q^{25} + 5 q^{26} + q^{29} + 2 q^{30} - q^{32} + 2 q^{33} + 5 q^{34} - q^{36} - 2 q^{37} + 4 q^{38} + 5 q^{40} - 2 q^{41} + 5 q^{45} + q^{49} - 3 q^{50} - 4 q^{52} + 3 q^{53} + 2 q^{54} - 4 q^{57} - q^{58} - 2 q^{61} - 2 q^{62} + q^{64} + 5 q^{65} - 2 q^{68} - q^{72} + 5 q^{73} - 2 q^{74} + 2 q^{78} - 4 q^{80} - 3 q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{93} - 2 q^{94} - 2 q^{96} + 5 q^{97} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(116))\)

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
116.1.b \(\chi_{116}(59, \cdot)\) None 0 1
116.1.d \(\chi_{116}(115, \cdot)\) 116.1.d.a 1 1
116.1.d.b 1
116.1.f \(\chi_{116}(17, \cdot)\) None 0 2
116.1.h \(\chi_{116}(35, \cdot)\) None 0 6
116.1.j \(\chi_{116}(7, \cdot)\) 116.1.j.a 6 6
116.1.k \(\chi_{116}(21, \cdot)\) None 0 12