Properties

Label 8039.2.a
Level 8039
Weight 2
Character orbit a
Rep. character \(\chi_{8039}(1,\cdot)\)
Character field \(\Q\)
Dimension 670
Newform subspaces 2
Sturm bound 1340
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8039 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8039.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(1340\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8039))\).

Total New Old
Modular forms 671 671 0
Cusp forms 670 670 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.

\(8039\)Dim.
\(+\)\(279\)
\(-\)\(391\)

Trace form

\( 670q + q^{2} + 673q^{4} + 2q^{5} + 6q^{7} - 3q^{8} + 676q^{9} + O(q^{10}) \) \( 670q + q^{2} + 673q^{4} + 2q^{5} + 6q^{7} - 3q^{8} + 676q^{9} - 2q^{10} + 4q^{11} - 16q^{12} + 8q^{13} - 10q^{14} + 675q^{16} + 4q^{17} - 3q^{18} + 18q^{19} - 8q^{20} + 18q^{21} + 16q^{22} + 4q^{23} + 4q^{24} + 684q^{25} + 12q^{26} - 18q^{27} + 36q^{28} + 10q^{29} + 16q^{30} + 4q^{31} + 5q^{32} + 14q^{33} + 22q^{34} - 18q^{35} + 721q^{36} + 12q^{37} + 2q^{38} + 4q^{39} + 16q^{40} + 12q^{41} + 26q^{42} + 14q^{43} + 20q^{44} - 8q^{45} + 62q^{46} - 20q^{47} - 22q^{48} + 690q^{49} - 11q^{50} + 12q^{51} + 16q^{52} - 6q^{53} + 14q^{54} + 2q^{55} - 22q^{56} + 44q^{57} + 16q^{58} - 18q^{59} - 18q^{60} + 32q^{61} + 12q^{62} - 2q^{63} + 683q^{64} + 30q^{65} + 2q^{66} + 22q^{67} - 42q^{68} - 14q^{69} - 20q^{70} - 12q^{71} - 15q^{72} + 42q^{73} - 38q^{74} - 34q^{75} + 60q^{76} + 30q^{77} - 38q^{78} + 42q^{79} - 26q^{80} + 718q^{81} - 32q^{82} + 20q^{83} + 88q^{84} + 70q^{85} + 18q^{86} + 14q^{87} + 8q^{88} + 22q^{89} - 46q^{90} + 26q^{91} - 36q^{92} + 16q^{93} - 4q^{94} - 26q^{95} + 14q^{96} + 42q^{97} + 13q^{98} + 92q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8039))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 8039
8039.2.a.a \(279\) \(64.192\) None \(-13\) \(-12\) \(-20\) \(-57\) \(+\)
8039.2.a.b \(391\) \(64.192\) None \(14\) \(12\) \(22\) \(63\) \(-\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database