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Properties

Label 3.72
Level 3
Weight 72
Dimension 11
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 48
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 72 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{72}(\Gamma_1(3))\).

Total New Old
Modular forms 25 11 14
Cusp forms 23 11 12
Eisenstein series 2 0 2

Trace form

\( 11 q - 97954934514 q^{2} - 50\!\cdots\!07 q^{3} + 12\!\cdots\!56 q^{4} + 11\!\cdots\!30 q^{5} + 23\!\cdots\!66 q^{6} - 66\!\cdots\!64 q^{7} - 51\!\cdots\!80 q^{8} + 27\!\cdots\!39 q^{9} + 23\!\cdots\!40 q^{10}+ \cdots + 58\!\cdots\!24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{72}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.72.a \(\chi_{3}(1, \cdot)\) 3.72.a.a 5 1
3.72.a.b 6

Decomposition of \(S_{72}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

\( S_{72}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{72}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)