Defining parameters
Level: | \( N \) | = | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 57.j (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 57 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newforms: | \( 2 \) | ||
Sturm bound: | \(13\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(57, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 54 | 0 |
Cusp forms | 30 | 30 | 0 |
Eisenstein series | 24 | 24 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(57, [\chi])\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
57.2.j.a | \(6\) | \(0.455\) | \(\Q(\zeta_{18})\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+2\zeta_{18}q^{4}+\cdots\) |
57.2.j.b | \(24\) | \(0.455\) | None | \(0\) | \(-9\) | \(0\) | \(-6\) |