Defining parameters
Level: | \( N \) | \(=\) | \( 356 = 2^{2} \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 356.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 356 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(45\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(356, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7 | 7 | 0 |
Cusp forms | 5 | 5 | 0 |
Eisenstein series | 2 | 2 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 5 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(356, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
356.1.d.a | $1$ | $0.178$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-89}) \) | \(\Q(\sqrt{89}) \) | \(-1\) | \(0\) | \(2\) | \(0\) | \(q-q^{2}+q^{4}+2q^{5}-q^{8}-q^{9}-2q^{10}+\cdots\) |
356.1.d.b | $1$ | $0.178$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-89}) \) | None | \(1\) | \(-1\) | \(-1\) | \(2\) | \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\) |
356.1.d.c | $1$ | $0.178$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-89}) \) | None | \(1\) | \(1\) | \(-1\) | \(-2\) | \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\) |
356.1.d.d | $2$ | $0.178$ | \(\Q(\sqrt{3}) \) | $D_{6}$ | \(\Q(\sqrt{-89}) \) | None | \(-2\) | \(0\) | \(-2\) | \(0\) | \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{8}+\cdots\) |