Defining parameters
Level: | \( N \) | \(=\) | \( 944 = 2^{4} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 944.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 59 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(944, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 5 | 19 |
Cusp forms | 18 | 4 | 14 |
Eisenstein series | 6 | 1 | 5 |
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 \(S_{1}^{\mathrm{new}}(944, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
944.1.h.a | $1$ | $0.471$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(1\) | \(-1\) | \(1\) | \(q+q^{3}-q^{5}+q^{7}-q^{15}+2q^{17}+q^{19}+\cdots\) |
944.1.h.b | $3$ | $0.471$ | \(\Q(\zeta_{18})^+\) | $D_{9}$ | \(\Q(\sqrt{-59}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(944, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(944, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(236, [\chi])\)\(^{\oplus 3}\)