Properties

Label 983.1.b
Level $983$
Weight $1$
Character orbit 983.b
Rep. character $\chi_{983}(982,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $3$
Sturm bound $82$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 983.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 983 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(82\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(983, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 13 13 0
Eisenstein series 1 1 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 13 0 0 0

Trace form

\( 13 q - q^{2} - q^{3} + 12 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 12 q^{9} + O(q^{10}) \) \( 13 q - q^{2} - q^{3} + 12 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 12 q^{9} - 3 q^{12} - 2 q^{14} + 11 q^{16} - 3 q^{18} - q^{19} - 2 q^{21} - q^{23} - 4 q^{24} + 13 q^{25} - 2 q^{27} - 3 q^{28} - q^{31} - 3 q^{32} + 9 q^{36} - q^{37} - 2 q^{38} - q^{41} - 4 q^{42} - q^{43} - 2 q^{46} - q^{47} - 5 q^{48} + 12 q^{49} - q^{50} - q^{53} - 4 q^{54} - 4 q^{56} - 2 q^{57} - q^{59} - 2 q^{62} - 3 q^{63} + 10 q^{64} - q^{67} - 2 q^{69} - 6 q^{72} - 2 q^{74} - q^{75} - 3 q^{76} - q^{79} + 11 q^{81} - 2 q^{82} - 6 q^{84} - 2 q^{86} - q^{89} - 3 q^{92} - 2 q^{93} - 2 q^{94} - 6 q^{96} - 3 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(983, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
983.1.b.a 983.b 983.b $1$ $0.491$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-983}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q-q^{2}-q^{3}+q^{6}-q^{7}+q^{8}+q^{14}+\cdots\)
983.1.b.b 983.b 983.b $3$ $0.491$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-983}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
983.1.b.c 983.b 983.b $9$ $0.491$ \(\Q(\zeta_{54})^+\) $D_{27}$ \(\Q(\sqrt{-983}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)