Properties

Label 8009.2.a
Level 8009
Weight 2
Character orbit a
Rep. character \(\chi_{8009}(1,\cdot)\)
Character field \(\Q\)
Dimension 667
Newforms 2
Sturm bound 1335
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8009 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8009.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(1335\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8009))\).

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.

\(8009\)Dim.
\(+\)\(306\)
\(-\)\(361\)

Trace form

\(667q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 667q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 657q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(667q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 667q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 657q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 663q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 23q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 18q^{20} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 667q^{25} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 12q^{28} \) \(\mathstrut -\mathstrut 20q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut -\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 625q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 26q^{40} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut +\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 24q^{44} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 679q^{49} \) \(\mathstrut -\mathstrut 13q^{50} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut -\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 8q^{54} \) \(\mathstrut +\mathstrut 32q^{55} \) \(\mathstrut -\mathstrut 64q^{56} \) \(\mathstrut -\mathstrut 14q^{57} \) \(\mathstrut +\mathstrut 12q^{58} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 34q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 40q^{63} \) \(\mathstrut +\mathstrut 707q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 40q^{68} \) \(\mathstrut -\mathstrut 28q^{69} \) \(\mathstrut +\mathstrut 32q^{70} \) \(\mathstrut -\mathstrut 26q^{71} \) \(\mathstrut -\mathstrut 39q^{72} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 16q^{75} \) \(\mathstrut +\mathstrut 72q^{76} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 22q^{78} \) \(\mathstrut +\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 60q^{80} \) \(\mathstrut +\mathstrut 587q^{81} \) \(\mathstrut +\mathstrut 44q^{82} \) \(\mathstrut +\mathstrut 38q^{83} \) \(\mathstrut -\mathstrut 68q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut +\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 78q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 86q^{92} \) \(\mathstrut -\mathstrut 28q^{93} \) \(\mathstrut +\mathstrut 24q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut 32q^{96} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 21q^{98} \) \(\mathstrut -\mathstrut 62q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8009))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 8009
8009.2.a.a \(306\) \(63.952\) None \(-13\) \(-25\) \(-25\) \(-102\) \(+\)
8009.2.a.b \(361\) \(63.952\) None \(10\) \(23\) \(21\) \(106\) \(-\)