Properties

Label 8017.2.a
Level 8017
Weight 2
Character orbit a
Rep. character \(\chi_{8017}(1,\cdot)\)
Character field \(\Q\)
Dimension 667
Newforms 2
Sturm bound 1336
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8017.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(1336\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8017))\).

Total New Old
Modular forms 668 668 0
Cusp forms 667 667 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.

\(8017\)Dim.
\(+\)\(327\)
\(-\)\(340\)

Trace form

\(667q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 665q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 663q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(667q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 665q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 663q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 28q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 657q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 22q^{24} \) \(\mathstrut +\mathstrut 643q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 34q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 33q^{32} \) \(\mathstrut -\mathstrut 22q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 641q^{36} \) \(\mathstrut -\mathstrut 26q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 26q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 20q^{42} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut -\mathstrut 18q^{44} \) \(\mathstrut -\mathstrut 10q^{45} \) \(\mathstrut +\mathstrut 18q^{46} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 68q^{48} \) \(\mathstrut +\mathstrut 661q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 38q^{52} \) \(\mathstrut -\mathstrut 16q^{53} \) \(\mathstrut -\mathstrut 38q^{54} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 62q^{56} \) \(\mathstrut -\mathstrut 24q^{57} \) \(\mathstrut -\mathstrut 52q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 609q^{64} \) \(\mathstrut -\mathstrut 18q^{65} \) \(\mathstrut -\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 30q^{67} \) \(\mathstrut +\mathstrut 22q^{68} \) \(\mathstrut +\mathstrut 36q^{69} \) \(\mathstrut -\mathstrut 80q^{70} \) \(\mathstrut +\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 39q^{72} \) \(\mathstrut -\mathstrut 28q^{73} \) \(\mathstrut -\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 32q^{75} \) \(\mathstrut -\mathstrut 22q^{76} \) \(\mathstrut +\mathstrut 12q^{77} \) \(\mathstrut -\mathstrut 56q^{78} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 635q^{81} \) \(\mathstrut -\mathstrut 44q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 92q^{84} \) \(\mathstrut -\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 36q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 144q^{88} \) \(\mathstrut +\mathstrut 14q^{89} \) \(\mathstrut -\mathstrut 24q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 34q^{93} \) \(\mathstrut -\mathstrut 44q^{94} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 44q^{96} \) \(\mathstrut -\mathstrut 40q^{97} \) \(\mathstrut -\mathstrut 51q^{98} \) \(\mathstrut -\mathstrut 42q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8017))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 8017
8017.2.a.a \(327\) \(64.016\) None \(-23\) \(-48\) \(-55\) \(-87\) \(+\)
8017.2.a.b \(340\) \(64.016\) None \(20\) \(44\) \(53\) \(81\) \(-\)