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Properties

Label 127.1
Level 127
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1344
Trace bound 0

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Defining parameters

Level: \( N \) = \( 127 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1344\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(127))\).

Total New Old
Modular forms 65 65 0
Cusp forms 2 2 0
Eisenstein series 63 63 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

\( 2 q - q^{2} + q^{4} - 2 q^{8} + 2 q^{9} + O(q^{10}) \) \( 2 q - q^{2} + q^{4} - 2 q^{8} + 2 q^{9} - q^{11} - q^{13} - q^{17} - q^{18} - q^{19} - 2 q^{22} + 2 q^{25} - 2 q^{26} - q^{31} + 2 q^{32} + 3 q^{34} + q^{36} - q^{37} + 3 q^{38} - q^{41} + 2 q^{44} - q^{47} + 2 q^{49} - q^{50} + 2 q^{52} - q^{61} + 3 q^{62} - q^{64} - 3 q^{68} - q^{71} - 2 q^{72} - q^{73} + 3 q^{74} - 3 q^{76} - q^{79} + 2 q^{81} - 2 q^{82} + q^{88} - 2 q^{94} - q^{98} - q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(127))\)

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
127.1.b \(\chi_{127}(126, \cdot)\) 127.1.b.a 2 1
127.1.d \(\chi_{127}(20, \cdot)\) None 0 2
127.1.g \(\chi_{127}(63, \cdot)\) None 0 6
127.1.h \(\chi_{127}(24, \cdot)\) None 0 6
127.1.j \(\chi_{127}(5, \cdot)\) None 0 12
127.1.l \(\chi_{127}(3, \cdot)\) None 0 36