Defining parameters
Level: | \( N \) | = | \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 32 \) | ||
Sturm bound: | \(241920\) | ||
Trace bound: | \(16\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1476))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 62080 | 28248 | 33832 |
Cusp forms | 58881 | 27544 | 31337 |
Eisenstein series | 3199 | 704 | 2495 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1476))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1476))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1476)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(369))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(738))\)\(^{\oplus 2}\)