Properties

Label 6037.2.a
Level 6037
Weight 2
Character orbit a
Rep. character \(\chi_{6037}(1,\cdot)\)
Character field \(\Q\)
Dimension 502
Newforms 2
Sturm bound 1006
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6037 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6037.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(1006\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6037))\).

Total New Old
Modular forms 503 503 0
Cusp forms 502 502 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.

\(6037\)Dim.
\(+\)\(243\)
\(-\)\(259\)

Trace form

\(502q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 502q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 500q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(502q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 502q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 500q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 514q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 18q^{18} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 18q^{22} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 494q^{25} \) \(\mathstrut -\mathstrut 14q^{26} \) \(\mathstrut -\mathstrut 14q^{27} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut +\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 510q^{36} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 30q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 38q^{44} \) \(\mathstrut -\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 32q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 484q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 12q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut +\mathstrut 26q^{58} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut -\mathstrut 26q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut -\mathstrut 50q^{63} \) \(\mathstrut +\mathstrut 562q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 10q^{68} \) \(\mathstrut -\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 114q^{70} \) \(\mathstrut -\mathstrut 20q^{71} \) \(\mathstrut -\mathstrut 16q^{72} \) \(\mathstrut +\mathstrut 18q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 52q^{75} \) \(\mathstrut +\mathstrut 28q^{76} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 42q^{80} \) \(\mathstrut +\mathstrut 486q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut -\mathstrut 52q^{84} \) \(\mathstrut +\mathstrut 18q^{85} \) \(\mathstrut +\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 40q^{87} \) \(\mathstrut +\mathstrut 96q^{88} \) \(\mathstrut +\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 32q^{90} \) \(\mathstrut -\mathstrut 46q^{91} \) \(\mathstrut +\mathstrut 42q^{92} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 76q^{94} \) \(\mathstrut -\mathstrut 28q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 72q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6037))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 6037
6037.2.a.a \(243\) \(48.206\) None \(-47\) \(-31\) \(-40\) \(-42\) \(+\)
6037.2.a.b \(259\) \(48.206\) None \(47\) \(29\) \(38\) \(42\) \(-\)