Defining parameters
Level: | \( N \) | = | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(20))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 118 | 65 | 53 |
Cusp forms | 98 | 57 | 41 |
Eisenstein series | 20 | 8 | 12 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(20))\)
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 \(S_{10}^{\mathrm{old}}(\Gamma_1(20))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(20)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)