Defining parameters
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.z (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 228 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(684, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 80 | 176 |
Cusp forms | 224 | 80 | 144 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(684, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
684.2.z.a | $8$ | $5.462$ | 8.0.\(\cdots\).3 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}-2\beta _{4}q^{4}-2\beta _{3}q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\) |
684.2.z.b | $72$ | $5.462$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(684, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)