Properties

Label 79.1.b
Level 79
Weight 1
Character orbit b
Rep. character \(\chi_{79}(78,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 79 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 79.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 79 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(79, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 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 2 0 0 0

Trace form

\(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut 3q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut q^{67} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut q^{73} \) \(\mathstrut +\mathstrut 2q^{76} \) \(\mathstrut +\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 2q^{92} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(79, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
79.1.b.a \(2\) \(0.039\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-79}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots\)