Defining parameters
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(280\) | ||
Trace bound: | \(22\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(294, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 28 | 212 |
Cusp forms | 208 | 28 | 180 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(294, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
294.5.c.a | $4$ | $30.391$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+8q^{4}+(-11\beta _{2}+\cdots)q^{5}+\cdots\) |
294.5.c.b | $8$ | $30.391$ | 8.0.339738624.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-2\beta _{1}q^{2}-3\beta _{2}q^{3}+8q^{4}+(5\beta _{4}-11\beta _{5}+\cdots)q^{5}+\cdots\) |
294.5.c.c | $8$ | $30.391$ | 8.0.339738624.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-2\beta _{1}q^{2}+\beta _{4}q^{3}+8q^{4}+(-5\beta _{2}+\cdots)q^{5}+\cdots\) |
294.5.c.d | $8$ | $30.391$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}-3\beta _{1}q^{3}+8q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(294, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)