Properties

Label 79.1.b
Level $79$
Weight $1$
Character orbit 79.b
Rep. character $\chi_{79}(78,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(79, [\chi])\) into newform subspaces

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 \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots\)