Defining parameters
Level: | \( N \) | = | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 24 \) | ||
Sturm bound: | \(464640\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1815))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 118720 | 79388 | 39332 |
Cusp forms | 113601 | 77700 | 35901 |
Eisenstein series | 5119 | 1688 | 3431 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1815))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(1815))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1815)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)