Defining parameters
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.l (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(378, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 168 | 16 | 152 |
Cusp forms | 120 | 16 | 104 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(378, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
378.2.l.a | $16$ | $3.018$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+(\beta _{1}+\beta _{7})q^{2}-q^{4}+(-\beta _{5}-\beta _{10}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(378, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)