Defining parameters
Level: | \( N \) | \(=\) | \( 578 = 2 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 578.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(153\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(578, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 94 | 22 | 72 |
Cusp forms | 58 | 22 | 36 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(578, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
578.2.b.a | $2$ | $4.615$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}+iq^{3}+q^{4}-iq^{6}-2iq^{7}+\cdots\) |
578.2.b.b | $2$ | $4.615$ | \(\Q(\sqrt{-2}) \) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}+\beta q^{3}+q^{4}+2\beta q^{5}-\beta q^{6}+\cdots\) |
578.2.b.c | $2$ | $4.615$ | \(\Q(\sqrt{-2}) \) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+3q^{9}+\beta q^{10}+\cdots\) |
578.2.b.d | $4$ | $4.615$ | 4.0.2048.2 | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+\beta _{1}q^{3}+q^{4}+2\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots\) |
578.2.b.e | $6$ | $4.615$ | 6.0.419904.1 | None | \(-6\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
578.2.b.f | $6$ | $4.615$ | 6.0.419904.1 | None | \(6\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+(\beta _{1}-\beta _{3}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(578, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(578, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)