Defining parameters
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(2\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(7, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3 | 3 | 0 |
Cusp forms | 1 | 1 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(7, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
7.3.b.a | $1$ | $0.191$ | \(\Q\) | \(\Q(\sqrt{-7}) \) | \(-3\) | \(0\) | \(0\) | \(-7\) | \(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\) |