Defining parameters
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.k (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(285, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 72 | 16 |
Cusp forms | 72 | 72 | 0 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(285, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
285.2.k.a | $4$ | $2.276$ | \(\Q(\zeta_{12})\) | None | \(-4\) | \(0\) | \(-4\) | \(-6\) | \(q+(-1+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2})q^{3}+\cdots\) |
285.2.k.b | $4$ | $2.276$ | \(\Q(\zeta_{12})\) | None | \(4\) | \(0\) | \(4\) | \(-6\) | \(q+(1+\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\) |
285.2.k.c | $28$ | $2.276$ | None | \(0\) | \(-2\) | \(0\) | \(0\) | ||
285.2.k.d | $36$ | $2.276$ | None | \(0\) | \(-2\) | \(0\) | \(4\) |