Defining parameters
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.bf (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 285 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 3 \) | ||
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 | 264 | 264 | 0 |
Cusp forms | 216 | 216 | 0 |
Eisenstein series | 48 | 48 | 0 |
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.bf.a | $12$ | $2.276$ | 12.0.\(\cdots\).1 | \(\Q(\sqrt{-15}) \) | \(-9\) | \(0\) | \(0\) | \(0\) | \(q+(-1+\beta _{4}-\beta _{5}-\beta _{6}+\beta _{11})q^{2}+\cdots\) |
285.2.bf.b | $12$ | $2.276$ | 12.0.\(\cdots\).1 | \(\Q(\sqrt{-15}) \) | \(9\) | \(0\) | \(0\) | \(0\) | \(q+(1-\beta _{4}-\beta _{5}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{11})q^{2}+\cdots\) |
285.2.bf.c | $192$ | $2.276$ | None | \(0\) | \(0\) | \(0\) | \(0\) |