Defining parameters
Level: | \( N \) | \(=\) | \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1584.i (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1584, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 600 | 40 | 560 |
Cusp forms | 552 | 40 | 512 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1584.3.i.a | $4$ | $43.161$ | \(\Q(\sqrt{-2}, \sqrt{-11})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{5}-2\beta _{1}q^{7}+\beta _{3}q^{11}+(-4+\cdots)q^{13}+\cdots\) |
1584.3.i.b | $8$ | $43.161$ | 8.0.\(\cdots\).6 | None | \(0\) | \(0\) | \(0\) | \(-16\) | \(q+(\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{7})q^{7}-\beta _{5}q^{11}+\cdots\) |
1584.3.i.c | $8$ | $43.161$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(16\) | \(q-\beta _{7}q^{5}+(2+\beta _{5})q^{7}+\beta _{3}q^{11}+(-1+\cdots)q^{13}+\cdots\) |
1584.3.i.d | $8$ | $43.161$ | 8.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(16\) | \(q+(2\beta _{1}+\beta _{5})q^{5}+(2-\beta _{2}+\beta _{4})q^{7}+\cdots\) |
1584.3.i.e | $12$ | $43.161$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(16\) | \(q+(-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{6})q^{7}-\beta _{3}q^{11}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)