Properties

Label 8039.2.a
Level 8039
Weight 2
Character orbit a
Rep. character \(\chi_{8039}(1,\cdot)\)
Character field \(\Q\)
Dimension 670
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8039))\) into irreducible Hecke orbits

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 \(14\) \(12\) \(22\) \(63\) \(-\)