Defining parameters
Level: | \( N \) | \(=\) | \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 936.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(936, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 176 | 60 | 116 |
Cusp forms | 160 | 60 | 100 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(936, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
936.2.g.a | $2$ | $7.474$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(0\) | \(0\) | \(6\) | \(q+(i+1)q^{2}+2 i q^{4}+3 i q^{5}+3 q^{7}+\cdots\) |
936.2.g.b | $4$ | $7.474$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(0\) | \(0\) | \(-12\) | \(q+(\beta_{2}-\beta_1)q^{2}+(\beta_{3}+\beta_1)q^{4}+(-2\beta_{3}+2\beta_1-2)q^{5}+\cdots\) |
936.2.g.c | $6$ | $7.474$ | 6.0.399424.1 | None | \(2\) | \(0\) | \(0\) | \(2\) | \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{5})q^{4}-\beta _{1}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\) |
936.2.g.d | $8$ | $7.474$ | \(\Q(\zeta_{20})\) | None | \(-2\) | \(0\) | \(0\) | \(4\) | \(q+\beta_{6} q^{2}-\beta_1 q^{4}+(\beta_{6}-\beta_{5}-\beta_{3}+\cdots+1)q^{5}+\cdots\) |
936.2.g.e | $16$ | $7.474$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-2\) | \(0\) | \(0\) | \(4\) | \(q-\beta _{10}q^{2}-\beta _{2}q^{4}-\beta _{14}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\) |
936.2.g.f | $24$ | $7.474$ | None | \(0\) | \(0\) | \(0\) | \(-8\) |
Decomposition of \(S_{2}^{\mathrm{old}}(936, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)