Properties

Label 4.24
Level 4
Weight 24
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 24
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 24 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(4))\).

Total New Old
Modular forms 13 2 11
Cusp forms 10 2 8
Eisenstein series 3 0 3

Trace form

\( 2 q + 170520 q^{3} - 92266020 q^{5} + 192083440 q^{7} + 8599879818 q^{9} - 1247174695800 q^{11} - 7460299980980 q^{13} - 106334360092080 q^{15} - 374897347903260 q^{17} - 840360279212552 q^{19} + 400401295079232 q^{21}+ \cdots - 98\!\cdots\!00 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(4))\)

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
4.24.a \(\chi_{4}(1, \cdot)\) 4.24.a.a 2 1

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(4))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_1(4)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)