Defining parameters
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(756, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 4 | 24 |
Cusp forms | 10 | 4 | 6 |
Eisenstein series | 18 | 0 | 18 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(756, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
756.1.d.a | $2$ | $0.377$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | None | \(\Q(\sqrt{21}) \) | \(0\) | \(0\) | \(0\) | \(-2\) | \(q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{17}+\cdots\) |
756.1.d.b | $2$ | $0.377$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(1\) | \(q-\zeta_{6}^{2}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(\zeta_{6}+\cdots)q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(756, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)