Defining parameters
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.f (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 19 \) | ||
Sturm bound: | \(162\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(324, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 100 | 140 |
Cusp forms | 192 | 92 | 100 |
Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(324, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(324, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)