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

Related objects

Downloads

Learn more about

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

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

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 \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)