↑

Properties

Label 2.80
Level 2
Weight 80
Dimension 7
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 20
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 80 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{80}(\Gamma_1(2))\).

Total New Old
Modular forms 21 7 14
Cusp forms 19 7 12
Eisenstein series 2 0 2

Trace form

\( 7 q - 549755813888 q^{2} - 18\!\cdots\!48 q^{3} + 21\!\cdots\!08 q^{4} - 61\!\cdots\!30 q^{5} - 49\!\cdots\!12 q^{6} + 40\!\cdots\!16 q^{7} - 16\!\cdots\!72 q^{8} + 10\!\cdots\!99 q^{9} - 10\!\cdots\!60 q^{10}+ \cdots - 23\!\cdots\!92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{80}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.80.a \(\chi_{2}(1, \cdot)\) 2.80.a.a 3 1
2.80.a.b 4

Decomposition of \(S_{80}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{80}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{80}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)