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

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

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 \(21\) \(29\) \(19\) \(52\) \(-\)