Defining parameters
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(14\) | ||
Distinguishing \(T_p\): | \(2\), \(59\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 264 | 48 | 216 |
Cusp forms | 216 | 48 | 168 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1575.2.g.a | $8$ | $12.576$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{6}q^{2}+\zeta_{24}^{3}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\) |
1575.2.g.b | $8$ | $12.576$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{6}q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{7}-2\zeta_{24}^{6}q^{8}+\cdots\) |
1575.2.g.c | $8$ | $12.576$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{6}q^{2}+\zeta_{24}^{3}q^{4}+(\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{7}+\cdots\) |
1575.2.g.d | $8$ | $12.576$ | 8.0.157351936.1 | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{6}q^{2}+(2+\beta _{5})q^{4}-\beta _{1}q^{7}+(\beta _{3}+\cdots)q^{8}+\cdots\) |
1575.2.g.e | $16$ | $12.576$ | 16.0.\(\cdots\).1 | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{10}q^{2}+(2+\beta _{4})q^{4}-\beta _{9}q^{7}+(\beta _{3}+\cdots)q^{8}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)