Defining parameters
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.e (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(187, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 32 | 8 |
Cusp forms | 32 | 32 | 0 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(187, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
187.2.e.a | $4$ | $1.493$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(-4\) | \(8\) | \(0\) | \(q+2\zeta_{8}^{2}q^{2}+(-1+2\zeta_{8}-\zeta_{8}^{2})q^{3}+\cdots\) |
187.2.e.b | $28$ | $1.493$ | None | \(0\) | \(4\) | \(-16\) | \(0\) |