Defining parameters
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.u (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 135 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 576 | 336 | 240 |
Cusp forms | 504 | 312 | 192 |
Eisenstein series | 72 | 24 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
675.2.u.a | $12$ | $5.390$ | \(\Q(\zeta_{36})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{36}^{5}+\zeta_{36}^{7}-\zeta_{36}^{9})q^{2}+(-2\zeta_{36}^{5}+\cdots)q^{3}+\cdots\) |
675.2.u.b | $24$ | $5.390$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
675.2.u.c | $60$ | $5.390$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
675.2.u.d | $84$ | $5.390$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
675.2.u.e | $132$ | $5.390$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)