Defining parameters
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(8\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(19, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7 | 7 | 0 |
Cusp forms | 5 | 5 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(19, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
19.5.b.a | $1$ | $1.964$ | \(\Q\) | \(\Q(\sqrt{-19}) \) | \(0\) | \(0\) | \(31\) | \(-73\) | \(q+2^{4}q^{4}+31q^{5}-73q^{7}+3^{4}q^{9}+\cdots\) |
19.5.b.b | $4$ | $1.964$ | 4.0.12107488.1 | None | \(0\) | \(0\) | \(-42\) | \(136\) | \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-3+3\beta _{2})q^{4}+\cdots\) |