Defining parameters
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.q (of order \(22\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 69 \) |
Character field: | \(\Q(\zeta_{22})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(690, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1520 | 320 | 1200 |
Cusp forms | 1360 | 320 | 1040 |
Eisenstein series | 160 | 0 | 160 |
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.q.a | $160$ | $5.510$ | None | \(0\) | \(0\) | \(-16\) | \(0\) | ||
690.2.q.b | $160$ | $5.510$ | None | \(0\) | \(0\) | \(16\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(690, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)