Defining parameters
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 408 | 24 | 384 |
Cusp forms | 360 | 24 | 336 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1008.3.d.a | $4$ | $27.466$ | \(\Q(\sqrt{-2}, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(2\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+(-4\beta _{1}+2\beta _{3})q^{11}+\cdots\) |
1008.3.d.b | $4$ | $27.466$ | \(\Q(\sqrt{-2}, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-3\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\) |
1008.3.d.c | $4$ | $27.466$ | \(\Q(\sqrt{-2}, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-2\beta _{1}-\beta _{2})q^{11}+\cdots\) |
1008.3.d.d | $4$ | $27.466$ | \(\Q(\sqrt{-2}, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots\) |
1008.3.d.e | $8$ | $27.466$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{2}-\beta _{4}+\beta _{5})q^{5}-\beta _{3}q^{7}+(\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)