Defining parameters
Level: | \( N \) | = | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 21 \) | ||
Newform subspaces: | \( 82 \) | ||
Sturm bound: | \(36000\) | ||
Trace bound: | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(550))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9560 | 2717 | 6843 |
Cusp forms | 8441 | 2717 | 5724 |
Eisenstein series | 1119 | 0 | 1119 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(550))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)