Defining parameters
| Level: | \( N \) | = | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 0 \) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(18000\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(550))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 582 | 0 | 582 |
| Cusp forms | 22 | 0 | 22 |
| Eisenstein series | 560 | 0 | 560 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 0 | 0 | 0 | 0 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(550))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(550)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 1}\)