Defining parameters
Level: | \( N \) | = | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 36.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 12 \) |
Character field: | \(\Q\) | ||
Newforms: | \( 1 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(36, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10 | 2 | 8 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(36, [\chi])\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
36.2.b.a | \(2\) | \(0.287\) | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{2}-2q^{4}-\beta q^{5}-2\beta q^{8}+2q^{10}+\cdots\) |