Properties

Label 6047.2.a
Level 6047
Weight 2
Character orbit a
Rep. character \(\chi_{6047}(1,\cdot)\)
Character field \(\Q\)
Dimension 504
Newforms 2
Sturm bound 1008
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(1008\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6047))\).

Total New Old
Modular forms 505 505 0
Cusp forms 504 504 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.

\(6047\)Dim.
\(+\)\(217\)
\(-\)\(287\)

Trace form

\( 504q + q^{2} + 2q^{3} + 503q^{4} - 2q^{6} + 4q^{7} + 3q^{8} + 504q^{9} + O(q^{10}) \) \( 504q + q^{2} + 2q^{3} + 503q^{4} - 2q^{6} + 4q^{7} + 3q^{8} + 504q^{9} - 8q^{10} + 8q^{12} + 6q^{13} - 8q^{14} - 2q^{15} + 497q^{16} - 2q^{17} + 5q^{18} - 4q^{19} - 14q^{20} - 10q^{21} + 6q^{22} + 8q^{23} - 10q^{24} + 518q^{25} + 10q^{26} + 14q^{27} + 16q^{28} - 8q^{29} - 24q^{30} + 4q^{31} + 17q^{32} + 6q^{33} - 4q^{34} - 42q^{35} + 485q^{36} + 34q^{37} - 16q^{38} - 10q^{39} - 20q^{40} + 18q^{41} - 32q^{42} - 2q^{43} + 26q^{44} + 4q^{45} - 14q^{46} + 12q^{47} + 26q^{48} + 506q^{49} + 43q^{50} + 8q^{51} + 6q^{52} - 8q^{53} - 16q^{55} - 28q^{56} + 42q^{57} + 58q^{58} - 6q^{59} - 54q^{60} - 2q^{61} + 8q^{62} - 12q^{63} + 519q^{64} + 4q^{65} - 22q^{66} + 26q^{67} + 26q^{68} + 2q^{69} - 2q^{70} - 32q^{71} + 15q^{72} + 46q^{73} + 16q^{74} - 14q^{75} - 2q^{76} - 14q^{77} + 68q^{78} + 26q^{79} - 22q^{80} + 520q^{81} + 2q^{82} + 26q^{83} + 22q^{84} + 12q^{85} + 54q^{86} - 14q^{87} + 4q^{88} + 10q^{89} + 14q^{92} + 34q^{93} - 40q^{94} - 8q^{95} - 10q^{96} + 56q^{97} + 45q^{98} + 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6047))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 6047
6047.2.a.a \(217\) \(48.286\) None \(-20\) \(-27\) \(-19\) \(-48\) \(+\)
6047.2.a.b \(287\) \(48.286\) None \(21\) \(29\) \(19\) \(52\) \(-\)