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Properties

Label 2.72
Level 2
Weight 72
Dimension 5
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 72 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{72}(\Gamma_1(2))\).

Total New Old
Modular forms 19 5 14
Cusp forms 17 5 12
Eisenstein series 2 0 2

Trace form

\( 5 q - 34359738368 q^{2} - 70\!\cdots\!88 q^{3} + 59\!\cdots\!20 q^{4} + 87\!\cdots\!50 q^{5} - 25\!\cdots\!80 q^{6} - 97\!\cdots\!24 q^{7} - 40\!\cdots\!32 q^{8} - 10\!\cdots\!15 q^{9} - 25\!\cdots\!00 q^{10}+ \cdots + 12\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{72}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.72.a \(\chi_{2}(1, \cdot)\) 2.72.a.a 2 1
2.72.a.b 3

Decomposition of \(S_{72}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{72}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{72}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)