Properties

Label 8011.2.a
Level 8011
Weight 2
Character orbit a
Rep. character \(\chi_{8011}(1,\cdot)\)
Character field \(\Q\)
Dimension 667
Newforms 2
Sturm bound 1335
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(1335\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8011))\).

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.

\(8011\)Dim.
\(+\)\(309\)
\(-\)\(358\)

Trace form

\(667q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 664q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 665q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(667q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 664q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 665q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 22q^{12} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 654q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 669q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 664q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 18q^{43} \) \(\mathstrut -\mathstrut 10q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut -\mathstrut 76q^{48} \) \(\mathstrut +\mathstrut 665q^{49} \) \(\mathstrut -\mathstrut 22q^{50} \) \(\mathstrut -\mathstrut 22q^{51} \) \(\mathstrut -\mathstrut 22q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 50q^{54} \) \(\mathstrut -\mathstrut 20q^{55} \) \(\mathstrut -\mathstrut 42q^{56} \) \(\mathstrut -\mathstrut 40q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 62q^{60} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 38q^{62} \) \(\mathstrut -\mathstrut 30q^{63} \) \(\mathstrut +\mathstrut 650q^{64} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 80q^{66} \) \(\mathstrut -\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 10q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 38q^{75} \) \(\mathstrut -\mathstrut 58q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut -\mathstrut 8q^{78} \) \(\mathstrut +\mathstrut 2q^{79} \) \(\mathstrut -\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 675q^{81} \) \(\mathstrut +\mathstrut 50q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 22q^{84} \) \(\mathstrut +\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 6q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut +\mathstrut 14q^{89} \) \(\mathstrut +\mathstrut 56q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut +\mathstrut 46q^{92} \) \(\mathstrut -\mathstrut 36q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut +\mathstrut 44q^{96} \) \(\mathstrut +\mathstrut 10q^{97} \) \(\mathstrut +\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8011))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 8011
8011.2.a.a \(309\) \(63.968\) None \(-33\) \(-15\) \(-74\) \(-19\) \(+\)
8011.2.a.b \(358\) \(63.968\) None \(33\) \(11\) \(76\) \(19\) \(-\)