Defining parameters
| Level: | \( N \) | \(=\) | \( 805 = 5 \cdot 7 \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 805.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 805 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(192\) | ||
| Trace bound: | \(3\) | ||
| Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(805, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 100 | 100 | 0 |
| Cusp forms | 92 | 92 | 0 |
| Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(805, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 805.2.d.a | $4$ | $6.428$ | \(\Q(\sqrt{-5}, \sqrt{23})\) | \(\Q(\sqrt{-115}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2q^{4}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}-3q^{9}+\cdots\) |
| 805.2.d.b | $8$ | $6.428$ | 8.0.40960000.1 | None | \(0\) | \(-8\) | \(0\) | \(0\) | \(q+(\beta _{4}-\beta _{5})q^{2}-q^{3}-\beta _{2}q^{4}+(\beta _{3}+2\beta _{7})q^{5}+\cdots\) |
| 805.2.d.c | $8$ | $6.428$ | 8.0.40960000.1 | None | \(0\) | \(8\) | \(0\) | \(0\) | \(q+(-\beta _{4}+\beta _{5})q^{2}+q^{3}-\beta _{2}q^{4}+(-2\beta _{3}+\cdots)q^{5}+\cdots\) |
| 805.2.d.d | $12$ | $6.428$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(-12\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}-q^{3}+(-2-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\) |
| 805.2.d.e | $12$ | $6.428$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(12\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+q^{3}+(-2-\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots\) |
| 805.2.d.f | $48$ | $6.428$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||