Defining parameters
| Level: | \( N \) | = | \( 2163 = 3 \cdot 7 \cdot 103 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 10 \) | ||
| Newform subspaces: | \( 12 \) | ||
| Sturm bound: | \(339456\) | ||
| Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2163))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2686 | 1182 | 1504 |
| Cusp forms | 238 | 170 | 68 |
| Eisenstein series | 2448 | 1012 | 1436 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 170 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2163))\)
We only show spaces with odd 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 \(S_{1}^{\mathrm{old}}(\Gamma_1(2163))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2163)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(309))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(721))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2163))\)\(^{\oplus 1}\)