Defining parameters
Level: | \( N \) | \(=\) | \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 330.u (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 55 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(330, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 640 | 96 | 544 |
Cusp forms | 512 | 96 | 416 |
Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(330, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
330.2.u.a | $48$ | $2.635$ | None | \(0\) | \(0\) | \(8\) | \(16\) | ||
330.2.u.b | $48$ | $2.635$ | None | \(0\) | \(0\) | \(8\) | \(24\) |
Decomposition of \(S_{2}^{\mathrm{old}}(330, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)