Defining parameters
| Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2880.m (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 120 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(1152\) | ||
| Trace bound: | \(19\) | ||
| Distinguishing \(T_p\): | \(7\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 624 | 48 | 576 |
| Cusp forms | 528 | 48 | 480 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 2880.2.m.a | $8$ | $22.997$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{7}+\zeta_{24}^{2}q^{11}+\cdots\) |
| 2880.2.m.b | $8$ | $22.997$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{7}+\zeta_{24}^{2}q^{11}+\cdots\) |
| 2880.2.m.c | $32$ | $22.997$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)