Defining parameters
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 285 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(285, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 44 | 0 |
Cusp forms | 36 | 36 | 0 |
Eisenstein series | 8 | 8 | 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.b.a | $4$ | $2.276$ | \(\Q(\sqrt{-3}, \sqrt{5})\) | \(\Q(\sqrt{-15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-3q^{6}+\cdots\) |
285.2.b.b | $16$ | $2.276$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | \(\Q(\sqrt{-95}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2+\beta _{7})q^{4}-\beta _{2}q^{5}+\cdots\) |
285.2.b.c | $16$ | $2.276$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{4}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\) |