Properties

Label 151.1
Level 151
Weight 1
Dimension 3
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1900
Trace bound 0

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Defining parameters

Level: \( N \) = \( 151 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1900\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(151))\).

Total New Old
Modular forms 78 78 0
Cusp forms 3 3 0
Eisenstein series 75 75 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q - q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + 3 q^{9} + O(q^{10}) \) \( 3 q - q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + q^{16} - q^{17} - q^{18} - q^{19} - 3 q^{20} - 2 q^{22} + 2 q^{25} - q^{29} - q^{31} - 3 q^{32} - 2 q^{34} + 2 q^{36} - q^{37} + 5 q^{38} + 3 q^{40} - q^{43} + 4 q^{44} - q^{45} - q^{47} + 3 q^{49} + 4 q^{50} - 2 q^{55} + 5 q^{58} - q^{59} - 2 q^{62} + 4 q^{68} - 2 q^{72} - 2 q^{74} - 3 q^{76} + 2 q^{80} + 3 q^{81} - 2 q^{85} - 2 q^{86} - 4 q^{88} - 2 q^{90} + 5 q^{94} - 2 q^{95} - q^{97} - q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(151))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
151.1.b \(\chi_{151}(150, \cdot)\) 151.1.b.a 3 1
151.1.e \(\chi_{151}(33, \cdot)\) None 0 2
151.1.f \(\chi_{151}(87, \cdot)\) None 0 4
151.1.i \(\chi_{151}(23, \cdot)\) None 0 8
151.1.j \(\chi_{151}(3, \cdot)\) None 0 20
151.1.l \(\chi_{151}(6, \cdot)\) None 0 40