Defining parameters
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(1080\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4012, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 546 | 86 | 460 |
Cusp forms | 534 | 86 | 448 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(4012, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
4012.2.b.a | $40$ | $32.036$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
4012.2.b.b | $46$ | $32.036$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(4012, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4012, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 3}\)