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Properties

Label 2.78
Level 2
Weight 78
Dimension 6
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 19
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 78 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(19\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{78}(\Gamma_1(2))\).

Total New Old
Modular forms 20 6 14
Cusp forms 18 6 12
Eisenstein series 2 0 2

Trace form

\( 6 q - 26\!\cdots\!80 q^{3} + 45\!\cdots\!16 q^{4} + 95\!\cdots\!60 q^{5} + 66\!\cdots\!24 q^{6} - 40\!\cdots\!60 q^{7} + 27\!\cdots\!58 q^{9} + 91\!\cdots\!60 q^{10} + 28\!\cdots\!52 q^{11} - 19\!\cdots\!80 q^{12}+ \cdots - 33\!\cdots\!64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{78}^{\mathrm{new}}(\Gamma_1(2))\)

We only show spaces with even 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
2.78.a \(\chi_{2}(1, \cdot)\) 2.78.a.a 3 1
2.78.a.b 3

Decomposition of \(S_{78}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{78}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{78}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)