Properties

Label 968.1.f
Level $968$
Weight $1$
Character orbit 968.f
Rep. character $\chi_{968}(243,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $132$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 968.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(968, [\chi])\).

Total New Old
Modular forms 16 13 3
Cusp forms 4 4 0
Eisenstein series 12 9 3

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

\( 4 q - 2 q^{3} + 4 q^{4} + 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{3} + 4 q^{4} + 2 q^{9} - 2 q^{12} + 4 q^{16} + 4 q^{25} - 4 q^{27} - 2 q^{34} + 2 q^{36} - 2 q^{38} - 2 q^{48} + 4 q^{49} - 2 q^{59} + 4 q^{64} - 2 q^{67} - 2 q^{75} - 2 q^{82} - 2 q^{86} - 2 q^{89} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(968, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
968.1.f.a 968.f 8.d $2$ $0.483$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-2}) \) None \(-2\) \(-1\) \(0\) \(0\) \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots\)
968.1.f.b 968.f 8.d $2$ $0.483$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-2}) \) None \(2\) \(-1\) \(0\) \(0\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)