Defining parameters
Level: | \( N \) | = | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 7 \) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(279936\) | ||
Trace bound: | \(25\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2268))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3473 | 624 | 2849 |
Cusp forms | 233 | 64 | 169 |
Eisenstein series | 3240 | 560 | 2680 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 64 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2268))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(2268))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2268)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 2}\)