Defining parameters
Level: | \( N \) | \(=\) | \( 163 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 163.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 163 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(41\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(163, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 29 | 29 | 0 |
Cusp forms | 27 | 27 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(163, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
163.3.b.a | $1$ | $4.441$ | \(\Q\) | \(\Q(\sqrt{-163}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+4q^{4}+9q^{9}+2^{4}q^{16}+5^{2}q^{25}+\cdots\) |
163.3.b.b | $26$ | $4.441$ | None | \(0\) | \(0\) | \(0\) | \(0\) |