Defining parameters
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.cx (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 180 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(720, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 624 | 144 | 480 |
Cusp forms | 528 | 144 | 384 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(720, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
720.2.cx.a | $8$ | $5.749$ | 8.0.12960000.1 | None | \(0\) | \(-2\) | \(8\) | \(-6\) | \(q+(-1+\beta _{4}+\beta _{6})q^{3}+(2-2\beta _{4}+\beta _{7})q^{5}+\cdots\) |
720.2.cx.b | $8$ | $5.749$ | 8.0.12960000.1 | None | \(0\) | \(2\) | \(8\) | \(6\) | \(q+(-\beta _{1}-\beta _{3})q^{3}+(-\beta _{1}+2\beta _{4})q^{5}+\cdots\) |
720.2.cx.c | $40$ | $5.749$ | None | \(0\) | \(-4\) | \(-8\) | \(6\) | ||
720.2.cx.d | $40$ | $5.749$ | None | \(0\) | \(4\) | \(-8\) | \(-6\) | ||
720.2.cx.e | $48$ | $5.749$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(720, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)