Defining parameters
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.t (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1216 | 80 | 1136 |
Cusp forms | 1088 | 80 | 1008 |
Eisenstein series | 128 | 0 | 128 |
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.t.a | $4$ | $22.997$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+2\zeta_{8}^{3})q^{7}+\cdots\) |
2880.2.t.b | $8$ | $22.997$ | 8.0.18939904.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(1+\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots\) |
2880.2.t.c | $16$ | $22.997$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{5}q^{5}+(-\beta _{1}+\beta _{4}+\beta _{7}-\beta _{8}-\beta _{10}+\cdots)q^{7}+\cdots\) |
2880.2.t.d | $20$ | $22.997$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{5}q^{5}-\beta _{13}q^{7}+(-\beta _{5}+\beta _{8})q^{11}+\cdots\) |
2880.2.t.e | $32$ | $22.997$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)