Defining parameters
| Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 690.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(288\) | ||
| Trace bound: | \(14\) | ||
| Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(690, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 152 | 20 | 132 |
| Cusp forms | 136 | 20 | 116 |
| Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(690, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 690.2.d.a | \(4\) | \(5.510\) | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}+q^{6}+\cdots\) |
| 690.2.d.b | \(4\) | \(5.510\) | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\) |
| 690.2.d.c | \(6\) | \(5.510\) | 6.0.350464.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots\) |
| 690.2.d.d | \(6\) | \(5.510\) | 6.0.5161984.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{4}q^{5}-q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(690, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)