Defining parameters
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(189\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(162, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 174 | 24 | 150 |
Cusp forms | 150 | 24 | 126 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(162, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
162.7.b.a | $4$ | $37.269$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q-4\beta _{1}q^{2}-2^{5}q^{4}+(70\beta _{1}-5^{2}\beta _{2}+\cdots)q^{5}+\cdots\) |
162.7.b.b | $8$ | $37.269$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(964\) | \(q+4\beta _{1}q^{2}-2^{5}q^{4}+(12\beta _{1}+\beta _{3})q^{5}+\cdots\) |
162.7.b.c | $12$ | $37.269$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-480\) | \(q+\beta _{2}q^{2}-2^{5}q^{4}+\beta _{8}q^{5}+(-40-\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(162, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)