Defining parameters
| Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(288\) | ||
| Trace bound: | \(7\) | ||
| Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(690, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 304 | 88 | 216 |
| Cusp forms | 272 | 88 | 184 |
| Eisenstein series | 32 | 0 | 32 |
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.i.a | \(4\) | \(5.510\) | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(-4\) | \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\) |
| 690.2.i.b | \(4\) | \(5.510\) | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(12\) | \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\) |
| 690.2.i.c | \(8\) | \(5.510\) | \(\Q(\zeta_{24})\) | None | \(0\) | \(-8\) | \(0\) | \(0\) | \(q-\zeta_{24}^{5}q^{2}+(-1+\zeta_{24}+\zeta_{24}^{3})q^{3}+\cdots\) |
| 690.2.i.d | \(8\) | \(5.510\) | 8.0.40960000.1 | None | \(0\) | \(-8\) | \(0\) | \(0\) | \(q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3})q^{3}-\beta _{3}q^{4}+\cdots\) |
| 690.2.i.e | \(32\) | \(5.510\) | None | \(0\) | \(4\) | \(0\) | \(-8\) | ||
| 690.2.i.f | \(32\) | \(5.510\) | None | \(0\) | \(4\) | \(0\) | \(8\) | ||
Decomposition of \(S_{2}^{\mathrm{old}}(690, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)