Defining parameters
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(2304\) | ||
Trace bound: | \(31\) | ||
Distinguishing \(T_p\): | \(5\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6048, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1200 | 96 | 1104 |
Cusp forms | 1104 | 96 | 1008 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(6048, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
6048.2.c.a | $2$ | $48.294$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+2iq^{5}+q^{7}-5iq^{13}-q^{17}+4iq^{19}+\cdots\) |
6048.2.c.b | $2$ | $48.294$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+2iq^{5}+q^{7}+5iq^{13}+q^{17}-4iq^{19}+\cdots\) |
6048.2.c.c | $8$ | $48.294$ | 8.0.3317760000.5 | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\beta _{6}q^{5}+q^{7}+(2\beta _{2}+\beta _{6})q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\) |
6048.2.c.d | $16$ | $48.294$ | \(\Q(\zeta_{40})\) | None | \(0\) | \(0\) | \(0\) | \(16\) | \(q+(\zeta_{40}^{11}+\zeta_{40}^{12})q^{5}+q^{7}-\zeta_{40}^{12}q^{11}+\cdots\) |
6048.2.c.e | $20$ | $48.294$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(20\) | \(q+\beta _{12}q^{5}+q^{7}+(-\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{11}+\cdots\) |
6048.2.c.f | $24$ | $48.294$ | None | \(0\) | \(0\) | \(0\) | \(-24\) | ||
6048.2.c.g | $24$ | $48.294$ | None | \(0\) | \(0\) | \(0\) | \(-24\) |
Decomposition of \(S_{2}^{\mathrm{old}}(6048, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6048, [\chi]) \cong \)