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Properties

Label 984.1.cj
Level $984$
Weight $1$
Character orbit 984.cj
Rep. character $\chi_{984}(11,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $32$
Newform subspaces $2$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 984 = 2^{3} \cdot 3 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 984.cj (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 984 \)
Character field: \(\Q(\zeta_{40})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(984, [\chi])\).

Total New Old
Modular forms 96 96 0
Cusp forms 32 32 0
Eisenstein series 64 64 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 0 0

Trace form

\( 32 q - 4 q^{3} - 4 q^{9} + O(q^{10}) \) \( 32 q - 4 q^{3} - 4 q^{9} + 8 q^{16} + 8 q^{22} - 4 q^{24} - 4 q^{27} - 4 q^{33} - 8 q^{34} - 16 q^{36} - 16 q^{48} + 8 q^{51} - 4 q^{54} - 32 q^{67} + 8 q^{76} + 8 q^{82} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(984, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
984.1.cj.a 984.cj 984.bj $16$ $0.491$ \(\Q(\zeta_{40})\) $D_{40}$ \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-\zeta_{40}^{13}q^{2}+\zeta_{40}^{8}q^{3}-\zeta_{40}^{6}q^{4}+\cdots\)
984.1.cj.b 984.cj 984.bj $16$ $0.491$ \(\Q(\zeta_{40})\) $D_{40}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{40}^{13}q^{2}+\zeta_{40}^{17}q^{3}-\zeta_{40}^{6}q^{4}+\cdots\)