Properties

Label 83.1.b
Level 83
Weight 1
Character orbit b
Rep. character \(\chi_{83}(82,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 83 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 83.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 83 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(83, [\chi])\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 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 1 0 0 0

Trace form

\( q - q^{3} + q^{4} - q^{7} + O(q^{10}) \) \( q - q^{3} + q^{4} - q^{7} - q^{11} - q^{12} + q^{16} - q^{17} + q^{21} + 2q^{23} + q^{25} + q^{27} - q^{28} - q^{29} - q^{31} + q^{33} - q^{37} + 2q^{41} - q^{44} - q^{48} + q^{51} - q^{59} - q^{61} + q^{64} - q^{68} - 2q^{69} - q^{75} + q^{77} - q^{81} + q^{83} + q^{84} + q^{87} + 2q^{92} + q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(83, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
83.1.b.a \(1\) \(0.041\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-83}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)