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Properties

Label 1607.1
Level 1607
Weight 1
Dimension 13
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 215204
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1607 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 3 \)
Sturm bound: \(215204\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1607))\).

Total New Old
Modular forms 816 816 0
Cusp forms 13 13 0
Eisenstein series 803 803 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 13 0 0 0

Trace form

\( 13 q - q^{2} - q^{3} + 12 q^{4} - 2 q^{6} - 2 q^{8} + 12 q^{9} + O(q^{10}) \) \( 13 q - q^{2} - q^{3} + 12 q^{4} - 2 q^{6} - 2 q^{8} + 12 q^{9} - 3 q^{12} + 11 q^{16} - q^{17} - 3 q^{18} - q^{23} - 4 q^{24} + 13 q^{25} - 2 q^{27} - q^{31} - 3 q^{32} - 2 q^{34} + 9 q^{36} - q^{37} - q^{41} - 2 q^{46} - 5 q^{48} + 13 q^{49} - q^{50} - 2 q^{51} - q^{53} - 4 q^{54} - q^{59} - 2 q^{62} + 10 q^{64} - q^{67} - 3 q^{68} - 2 q^{69} - 6 q^{72} - q^{73} - 2 q^{74} - q^{75} - q^{79} + 11 q^{81} - 2 q^{82} - q^{89} - 3 q^{92} - 2 q^{93} - 6 q^{96} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1607))\)

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
1607.1.b \(\chi_{1607}(1606, \cdot)\) 1607.1.b.a 1 1
1607.1.b.b 3
1607.1.b.c 9
1607.1.d \(\chi_{1607}(85, \cdot)\) None 0 10
1607.1.f \(\chi_{1607}(15, \cdot)\) None 0 72
1607.1.h \(\chi_{1607}(5, \cdot)\) None 0 720