Defining parameters
Level: | \( N \) | = | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(15))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 54 | 26 |
Cusp forms | 64 | 46 | 18 |
Eisenstein series | 16 | 8 | 8 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(15))\)
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 \(S_{10}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)