Defining parameters
Level: | \( N \) | \(=\) | \( 242 = 2 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 242.c (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(242, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 444 | 108 | 336 |
Cusp forms | 348 | 108 | 240 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(242, [\chi])\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(242, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(242, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)