Defining parameters
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(392\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(5\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(294, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 352 | 82 | 270 |
Cusp forms | 320 | 82 | 238 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(294, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
294.7.b.a | $2$ | $67.636$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(-42\) | \(0\) | \(0\) | \(q+\beta q^{2}+(-21-3\beta )q^{3}-2^{5}q^{4}+30\beta q^{5}+\cdots\) |
294.7.b.b | $12$ | $67.636$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-2^{5}q^{4}+(\beta _{2}+\beta _{11})q^{5}+\cdots\) |
294.7.b.c | $12$ | $67.636$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(84\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+(7+\beta _{2})q^{3}-2^{5}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\) |
294.7.b.d | $16$ | $67.636$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2^{5}q^{4}+(\beta _{2}-\beta _{5}+\cdots)q^{5}+\cdots\) |
294.7.b.e | $16$ | $67.636$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{3}q^{3}-2^{5}q^{4}+(-\beta _{1}+\beta _{9}+\cdots)q^{5}+\cdots\) |
294.7.b.f | $24$ | $67.636$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{7}^{\mathrm{old}}(294, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)