Defining parameters
Level: | \( N \) | \(=\) | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 57.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 57 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(13\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(57, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8 | 8 | 0 |
Cusp forms | 4 | 4 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(57, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
57.2.d.a | $4$ | $0.455$ | \(\Q(\sqrt{2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{3})q^{6}+\cdots\) |