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Properties

Label 7.67
Level 7
Weight 67
Dimension 129
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 268
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 67 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(268\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{67}(\Gamma_1(7))\).

Total New Old
Modular forms 135 135 0
Cusp forms 129 129 0
Eisenstein series 6 6 0

Trace form

\( 129 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 11\!\cdots\!65 q^{5} + 21\!\cdots\!77 q^{7} + 23\!\cdots\!49 q^{8} - 71\!\cdots\!31 q^{9} + 72\!\cdots\!80 q^{10} + 49\!\cdots\!73 q^{11} - 24\!\cdots\!36 q^{12} - 29\!\cdots\!31 q^{14}+ \cdots - 77\!\cdots\!62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{67}^{\mathrm{new}}(\Gamma_1(7))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.67.b \(\chi_{7}(6, \cdot)\) 7.67.b.a 1 1
7.67.b.b 42
7.67.d \(\chi_{7}(3, \cdot)\) 7.67.d.a 86 2