Defining parameters
Level: | \( N \) | = | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | = | \( 12 \) |
Nonzero newspaces: | \( 3 \) | ||
Newforms: | \( 5 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(20))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 142 | 79 | 63 |
Cusp forms | 122 | 71 | 51 |
Eisenstein series | 20 | 8 | 12 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(20))\)
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 the newforms together with their dimension.
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)