Properties

Label 944.1.h
Level $944$
Weight $1$
Character orbit 944.h
Rep. character $\chi_{944}(353,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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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

\( 4 q + q^{3} - q^{5} + q^{7} + 3 q^{9} + O(q^{10}) \) \( 4 q + q^{3} - q^{5} + q^{7} + 3 q^{9} + 2 q^{15} - q^{17} + q^{19} - 2 q^{21} + 3 q^{25} + 2 q^{27} - q^{29} + 2 q^{35} - q^{41} - 3 q^{45} + 3 q^{49} + 2 q^{51} - q^{53} - 2 q^{57} - 4 q^{59} - 6 q^{63} + q^{71} - 6 q^{75} + q^{79} + 2 q^{81} - 2 q^{85} + 2 q^{87} - 7 q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(944, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
944.1.h.a 944.h 59.b $1$ $0.471$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-59}) \) None \(0\) \(1\) \(-1\) \(1\) \(q+q^{3}-q^{5}+q^{7}-q^{15}+2q^{17}+q^{19}+\cdots\)
944.1.h.b 944.h 59.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

\( S_{1}^{\mathrm{old}}(944, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(236, [\chi])\)\(^{\oplus 3}\)