Defining parameters
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 136 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(306\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2312, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26 | 20 | 6 |
Cusp forms | 8 | 6 | 2 |
Eisenstein series | 18 | 14 | 4 |
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 \(S_{1}^{\mathrm{new}}(2312, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2312.1.e.a | $2$ | $1.154$ | \(\Q(\sqrt{-2}) \) | $D_{4}$ | \(\Q(\sqrt{-2}) \) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}-q^{9}+\cdots\) |
2312.1.e.b | $4$ | $1.154$ | 4.0.2048.2 | $D_{8}$ | \(\Q(\sqrt{-2}) \) | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2312, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2312, [\chi]) \cong \)