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Properties

Label 83.2.a
Level $83$
Weight $2$
Character orbit 83.a
Rep. character $\chi_{83}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
Sturm bound $14$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 83.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(83))\).

Total New Old
Modular forms 8 8 0
Cusp forms 7 7 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.

\(83\)Dim
\(+\)\(1\)
\(-\)\(6\)

Trace form

\( 7 q + 6 q^{4} - 6 q^{6} + 6 q^{8} + q^{9} + O(q^{10}) \) \( 7 q + 6 q^{4} - 6 q^{6} + 6 q^{8} + q^{9} - 4 q^{10} - 8 q^{12} + 8 q^{13} - 12 q^{14} - 4 q^{15} - 10 q^{18} - 2 q^{19} - 18 q^{20} + q^{21} - 4 q^{22} - 9 q^{23} - 20 q^{24} + 13 q^{25} + 4 q^{26} + 15 q^{27} + 12 q^{28} - 8 q^{29} + 16 q^{30} + 8 q^{31} + 12 q^{32} - q^{33} + 10 q^{34} - 4 q^{35} - 6 q^{36} + 28 q^{37} - 8 q^{38} - 2 q^{39} - 24 q^{40} - 3 q^{41} + 14 q^{42} - 16 q^{43} + 24 q^{44} + 14 q^{45} - 8 q^{46} - 12 q^{47} + 8 q^{48} + 13 q^{49} + 36 q^{50} - 29 q^{51} + 42 q^{52} + 20 q^{53} + 14 q^{54} - 30 q^{55} - 32 q^{56} - 12 q^{57} + 32 q^{58} - 12 q^{59} - 2 q^{60} - 5 q^{63} + 16 q^{64} + 4 q^{65} - 36 q^{66} + 14 q^{67} - 20 q^{68} + 12 q^{69} - 16 q^{70} - 24 q^{71} + 4 q^{72} - 6 q^{73} + 34 q^{74} - 44 q^{75} - 30 q^{76} - 3 q^{77} - 24 q^{78} + 2 q^{79} - 58 q^{80} - 33 q^{81} + 12 q^{82} + 5 q^{83} + 38 q^{84} + 8 q^{85} + 24 q^{86} + 4 q^{87} - 8 q^{88} - 22 q^{89} - 8 q^{90} + 16 q^{91} + 6 q^{92} + 29 q^{93} - 8 q^{94} - 8 q^{95} - 14 q^{96} - 2 q^{97} - 32 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(83))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 83
83.2.a.a 83.a 1.a $1$ $0.663$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots\)
83.2.a.b 83.a 1.a $6$ $0.663$ 6.6.9059636.1 None \(1\) \(1\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{3}q^{3}+(1-\beta _{5})q^{4}+\cdots\)