Defining parameters
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 228 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2736, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 12 | 28 |
Cusp forms | 16 | 12 | 4 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2736.1.b.a | $4$ | $1.365$ | \(\Q(\zeta_{8})\) | $D_{4}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots\) |
2736.1.b.b | $8$ | $1.365$ | \(\Q(\zeta_{24})\) | $D_{12}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)