Defining parameters
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.n (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 84 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(13\), \(19\), \(67\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(588, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 176 | 80 |
Cusp forms | 192 | 144 | 48 |
Eisenstein series | 64 | 32 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(588, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
588.2.n.a | $4$ | $4.695$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | \(\Q(\sqrt{-21}) \) | \(0\) | \(-6\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\) |
588.2.n.b | $4$ | $4.695$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | \(\Q(\sqrt{-21}) \) | \(0\) | \(6\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
588.2.n.c | $16$ | $4.695$ | 16.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots\) |
588.2.n.d | $24$ | $4.695$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
588.2.n.e | $24$ | $4.695$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
588.2.n.f | $24$ | $4.695$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
588.2.n.g | $24$ | $4.695$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
588.2.n.h | $24$ | $4.695$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(588, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)