Defining parameters
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(29\) | ||
Distinguishing \(T_p\): | \(7\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 624 | 32 | 592 |
Cusp forms | 528 | 32 | 496 |
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.b.a | $8$ | $22.997$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(-8\) | \(0\) | \(q-q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\beta _{2}q^{13}+\cdots\) |
2880.2.b.b | $8$ | $22.997$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(-8\) | \(0\) | \(q-q^{5}-\zeta_{24}^{5}q^{7}+\zeta_{24}^{5}q^{11}+\zeta_{24}q^{13}+\cdots\) |
2880.2.b.c | $8$ | $22.997$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(8\) | \(0\) | \(q+q^{5}-\zeta_{24}^{6}q^{7}-\zeta_{24}^{6}q^{11}-\zeta_{24}q^{13}+\cdots\) |
2880.2.b.d | $8$ | $22.997$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(8\) | \(0\) | \(q+q^{5}+\beta _{3}q^{7}+(\beta _{1}-\beta _{3})q^{11}-\beta _{2}q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)