Defining parameters
Level: | \( N \) | \(=\) | \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 936.o (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 104 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(936, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 8 | 12 |
Cusp forms | 12 | 6 | 6 |
Eisenstein series | 8 | 2 | 6 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(936, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
936.1.o.a | $1$ | $0.467$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-26}) \) | None | \(-1\) | \(0\) | \(1\) | \(-1\) | \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\) |
936.1.o.b | $1$ | $0.467$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-26}) \) | None | \(1\) | \(0\) | \(-1\) | \(1\) | \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\) |
936.1.o.c | $4$ | $0.467$ | \(\Q(\zeta_{8})\) | $D_{4}$ | \(\Q(\sqrt{-39}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(936, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(936, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)