Defining parameters
Level: | \( N \) | \(=\) | \( 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 229.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 229 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(38\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(229, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 18 | 18 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(229, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
229.2.b.a | $2$ | $1.829$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(2\) | \(6\) | \(0\) | \(q+\beta q^{2}+q^{3}-3q^{4}+3q^{5}+\beta q^{6}+\cdots\) |
229.2.b.b | $16$ | $1.829$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(-12\) | \(0\) | \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-1-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\) |