Defining parameters
Level: | \( N \) | = | \( 473 = 11 \cdot 43 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Newform subspaces: | \( 33 \) | ||
Sturm bound: | \(36960\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(473))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9660 | 9445 | 215 |
Cusp forms | 8821 | 8705 | 116 |
Eisenstein series | 839 | 740 | 99 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(473))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(473))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(473)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)