Properties

Label 79.2.a
Level $79$
Weight $2$
Character orbit 79.a
Rep. character $\chi_{79}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $13$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 79.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(13\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(79))\).

Total New Old
Modular forms 7 7 0
Cusp forms 6 6 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(79\)Dim
\(+\)\(1\)
\(-\)\(5\)

Trace form

\( 6 q - q^{2} + q^{4} + 4 q^{5} - 6 q^{7} + 3 q^{8} + 8 q^{9} + O(q^{10}) \) \( 6 q - q^{2} + q^{4} + 4 q^{5} - 6 q^{7} + 3 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{12} + 2 q^{14} - 10 q^{15} - 13 q^{16} + 4 q^{17} - 23 q^{18} + 9 q^{20} - 6 q^{21} + q^{22} + 4 q^{23} - 2 q^{24} + 10 q^{25} + 13 q^{26} + 12 q^{27} - 14 q^{28} + 4 q^{30} - 8 q^{31} - 2 q^{33} - 2 q^{34} + 4 q^{35} + 19 q^{36} - 2 q^{37} - 4 q^{38} - 14 q^{39} + q^{40} + 20 q^{41} + 26 q^{42} - 10 q^{43} + 12 q^{44} + 26 q^{45} + 12 q^{47} + 2 q^{48} - 4 q^{49} - 18 q^{50} + 8 q^{51} + 12 q^{52} + 10 q^{53} - 16 q^{54} - 12 q^{55} - 14 q^{56} - 34 q^{57} + 38 q^{58} + 2 q^{59} - 30 q^{60} - 10 q^{61} + 25 q^{62} - 42 q^{63} - q^{64} - 14 q^{65} + 36 q^{66} - 8 q^{67} - 22 q^{69} - 2 q^{70} + 18 q^{71} + 21 q^{72} - 10 q^{73} - 20 q^{74} - 42 q^{75} + 13 q^{76} - 14 q^{77} - 28 q^{78} + 4 q^{79} - 6 q^{80} + 30 q^{81} + 18 q^{82} - 36 q^{83} + 2 q^{84} + 26 q^{85} - 6 q^{86} + 24 q^{87} - 22 q^{88} + 40 q^{89} - 54 q^{90} - 22 q^{91} - q^{92} + 6 q^{93} + 2 q^{94} - 24 q^{95} + 8 q^{96} - 20 q^{97} - 3 q^{98} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(79))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 79
79.2.a.a 79.a 1.a $1$ $0.631$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
79.2.a.b 79.a 1.a $5$ $0.631$ 5.5.81589.1 None \(0\) \(1\) \(7\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)