Defining parameters
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.k (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(441, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 168 | 72 |
Cusp forms | 208 | 152 | 56 |
Eisenstein series | 32 | 16 | 16 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(441, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
441.3.k.a | $28$ | $12.016$ | None | \(-2\) | \(0\) | \(0\) | \(0\) | ||
441.3.k.b | $28$ | $12.016$ | None | \(1\) | \(3\) | \(0\) | \(0\) | ||
441.3.k.c | $96$ | $12.016$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(441, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)