Defining parameters
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.k (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
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 | 216 | 40 | 176 |
Cusp forms | 144 | 32 | 112 |
Eisenstein series | 72 | 8 | 64 |
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.k.a | $4$ | $5.390$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{4}+3\zeta_{12}q^{7}-3\zeta_{12}^{3}q^{8}+\cdots\) |
675.2.k.b | $12$ | $5.390$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{8}q^{2}+(2\beta _{6}-\beta _{9})q^{4}+(-\beta _{3}+\beta _{7}+\cdots)q^{7}+\cdots\) |
675.2.k.c | $16$ | $5.390$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{7}+\beta _{11})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)