Defining parameters
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(288, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 160 | 16 | 144 |
Cusp forms | 128 | 14 | 114 |
Eisenstein series | 32 | 2 | 30 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(288, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
288.4.d.a | $2$ | $16.993$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(16\) | \(q-2\beta q^{5}+8q^{7}+3\beta q^{11}-10\beta q^{13}+\cdots\) |
288.4.d.b | $2$ | $16.993$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-6}) \) | \(0\) | \(0\) | \(0\) | \(68\) | \(q+7\beta q^{5}+34q^{7}+2\beta q^{11}-267q^{25}+\cdots\) |
288.4.d.c | $4$ | $16.993$ | \(\Q(\sqrt{-10}, \sqrt{22})\) | None | \(0\) | \(0\) | \(0\) | \(-40\) | \(q+\beta _{1}q^{5}-10q^{7}-6\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots\) |
288.4.d.d | $6$ | $16.993$ | 6.0.8248384.1 | None | \(0\) | \(0\) | \(0\) | \(-28\) | \(q-\beta _{2}q^{5}+(-5-\beta _{1})q^{7}+(-2\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(288, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(288, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)