Defining parameters
Level: | \( N \) | \(=\) | \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1224.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\), \(47\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1224, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 664 | 68 | 596 |
Cusp forms | 632 | 68 | 564 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)