Defining parameters
| Level: | \( N \) | = | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | = | \( 8 \) |
| Nonzero newspaces: | \( 12 \) | ||
| Sturm bound: | \(86400\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(450))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 38248 | 9193 | 29055 |
| Cusp forms | 37352 | 9193 | 28159 |
| Eisenstein series | 896 | 0 | 896 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(450))\)
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 \(S_{8}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(450)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)