Properties

Label 961.1.h
Level $961$
Weight $1$
Character orbit 961.h
Rep. character $\chi_{961}(115,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8$
Newform subspaces $1$
Sturm bound $82$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 961 = 31^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 961.h (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(82\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(961, [\chi])\).

Total New Old
Modular forms 136 120 16
Cusp forms 8 8 0
Eisenstein series 128 112 16

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 2 q^{2} + 4 q^{5} - q^{7} - 2 q^{8} + q^{9} + O(q^{10}) \) \( 8 q + 2 q^{2} + 4 q^{5} - q^{7} - 2 q^{8} + q^{9} + q^{10} + q^{14} + 2 q^{16} - q^{18} - q^{19} - 2 q^{35} + q^{38} - q^{40} - q^{41} - q^{45} - 4 q^{47} + 4 q^{56} - q^{59} - 8 q^{63} - 2 q^{64} - 8 q^{67} + 2 q^{70} - q^{71} + q^{72} + q^{80} + q^{81} + q^{82} + q^{90} - 16 q^{94} - 2 q^{95} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(961, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
961.1.h.a 961.h 31.h $8$ $0.480$ \(\Q(\zeta_{15})\) $D_{3}$ \(\Q(\sqrt{-31}) \) None 31.1.b.a \(2\) \(0\) \(4\) \(-1\) \(q+\zeta_{30}^{3}q^{2}-\zeta_{30}^{10}q^{5}+\zeta_{30}^{11}q^{7}+\cdots\)