Properties

Label 6037.2.a
Level 6037
Weight 2
Character orbit a
Rep. character \(\chi_{6037}(1,\cdot)\)
Character field \(\Q\)
Dimension 502
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6037))\) into newform subspaces

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 \(47\) \(29\) \(38\) \(42\) \(-\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database