Defining parameters
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.bo (of order \(7\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
Character field: | \(\Q(\zeta_{7})\) | ||
Sturm bound: | \(1792\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(2352, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8136 | 1008 | 7128 |
Cusp forms | 7992 | 1008 | 6984 |
Eisenstein series | 144 | 0 | 144 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)