Defining parameters
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.cn (of order \(78\) and degree \(24\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 169 \) |
Character field: | \(\Q(\zeta_{78})\) | ||
Sturm bound: | \(1092\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3380, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13248 | 1440 | 11808 |
Cusp forms | 12960 | 1440 | 11520 |
Eisenstein series | 288 | 0 | 288 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3380, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3380, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)