Defining parameters
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.cf (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 76 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(684, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 768 | 312 | 456 |
Cusp forms | 672 | 288 | 384 |
Eisenstein series | 96 | 24 | 72 |
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.cf.a | $48$ | $5.462$ | None | \(6\) | \(0\) | \(12\) | \(0\) | ||
684.2.cf.b | $60$ | $5.462$ | None | \(-3\) | \(0\) | \(0\) | \(0\) | ||
684.2.cf.c | $60$ | $5.462$ | None | \(3\) | \(0\) | \(0\) | \(0\) | ||
684.2.cf.d | $120$ | $5.462$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(684, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)