Defining parameters
Level: | \( N \) | = | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 40 \) | ||
Sturm bound: | \(1362816\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3380))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 345264 | 181261 | 164003 |
Cusp forms | 336145 | 178805 | 157340 |
Eisenstein series | 9119 | 2456 | 6663 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3380))\)
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 the newforms together with their dimension.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3380))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(3380)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1690))\)\(^{\oplus 2}\)