Defining parameters
Level: | \( N \) | = | \( 451 = 11 \cdot 41 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 28 \) | ||
Newform subspaces: | \( 34 \) | ||
Sturm bound: | \(33600\) | ||
Trace bound: | \(12\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(451))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8800 | 8601 | 199 |
Cusp forms | 8001 | 7897 | 104 |
Eisenstein series | 799 | 704 | 95 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(451))\)
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.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(451))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(451)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(451))\)\(^{\oplus 1}\)