Properties

Label 7.3
Level 7
Weight 3
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(7))\).

Total New Old
Modular forms 7 7 0
Cusp forms 1 1 0
Eisenstein series 6 6 0

Trace form

\( q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} + O(q^{10}) \) \( q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} - 6q^{11} + 21q^{14} - 11q^{16} - 27q^{18} + 18q^{22} + 18q^{23} + 25q^{25} - 35q^{28} - 54q^{29} + 45q^{32} + 45q^{36} - 38q^{37} + 58q^{43} - 30q^{44} - 54q^{46} + 49q^{49} - 75q^{50} - 6q^{53} + 21q^{56} + 162q^{58} - 63q^{63} - 91q^{64} - 118q^{67} + 114q^{71} - 27q^{72} + 114q^{74} + 42q^{77} - 94q^{79} + 81q^{81} - 174q^{86} + 18q^{88} + 90q^{92} - 147q^{98} - 54q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.3.b \(\chi_{7}(6, \cdot)\) 7.3.b.a 1 1
7.3.d \(\chi_{7}(3, \cdot)\) None 0 2