Defining parameters
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(432\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(690, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 592 | 88 | 504 |
Cusp forms | 560 | 88 | 472 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(690, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
690.3.k.a | $40$ | $18.801$ | None | \(40\) | \(0\) | \(-8\) | \(-8\) | ||
690.3.k.b | $48$ | $18.801$ | None | \(-48\) | \(0\) | \(-8\) | \(-8\) |
Decomposition of \(S_{3}^{\mathrm{old}}(690, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)