Defining parameters
| Level: | \( N \) | = | \( 213 = 3 \cdot 71 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 0 \) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(3360\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(213))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 146 | 68 | 78 |
| Cusp forms | 6 | 0 | 6 |
| Eisenstein series | 140 | 68 | 72 |
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(213))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(213)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(213))\)\(^{\oplus 1}\)