Defining parameters
Level: | \( N \) | \(=\) | \( 592 = 2^{4} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 592.bc (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(152\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(592, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 492 | 120 | 372 |
Cusp forms | 420 | 108 | 312 |
Eisenstein series | 72 | 12 | 60 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(592, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
592.2.bc.a | $6$ | $4.727$ | \(\Q(\zeta_{18})\) | None | \(0\) | \(-3\) | \(-6\) | \(-3\) | \(q+(-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-2\zeta_{18}^{3}+\cdots)q^{5}+\cdots\) |
592.2.bc.b | $6$ | $4.727$ | \(\Q(\zeta_{18})\) | None | \(0\) | \(3\) | \(3\) | \(-6\) | \(q+(\zeta_{18}+\zeta_{18}^{3})q^{3}+(1+\zeta_{18}+2\zeta_{18}^{2}+\cdots)q^{5}+\cdots\) |
592.2.bc.c | $6$ | $4.727$ | \(\Q(\zeta_{18})\) | None | \(0\) | \(6\) | \(6\) | \(12\) | \(q+(1+\zeta_{18}^{4})q^{3}+(1+\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\) |
592.2.bc.d | $12$ | $4.727$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(3\) | \(-6\) | \(-6\) | \(q+(\beta _{1}+\beta _{9})q^{3}+(-1+\beta _{1}+\beta _{5})q^{5}+\cdots\) |
592.2.bc.e | $24$ | $4.727$ | None | \(0\) | \(-3\) | \(-3\) | \(9\) | ||
592.2.bc.f | $24$ | $4.727$ | None | \(0\) | \(0\) | \(3\) | \(3\) | ||
592.2.bc.g | $30$ | $4.727$ | None | \(0\) | \(0\) | \(-6\) | \(3\) |
Decomposition of \(S_{2}^{\mathrm{old}}(592, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(592, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)