Properties

Label 6043.2.a
Level 6043
Weight 2
Character orbit a
Rep. character \(\chi_{6043}(1,\cdot)\)
Character field \(\Q\)
Dimension 503
Newform subspaces 3
Sturm bound 1007
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6043 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6043.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(1007\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6043))\).

Total New Old
Modular forms 504 504 0
Cusp forms 503 503 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.

\(6043\)Dim.
\(+\)\(243\)
\(-\)\(260\)

Trace form

\( 503q - 2q^{2} - 4q^{3} + 502q^{4} - 2q^{5} - 4q^{7} + 497q^{9} + O(q^{10}) \) \( 503q - 2q^{2} - 4q^{3} + 502q^{4} - 2q^{5} - 4q^{7} + 497q^{9} + 12q^{10} - 4q^{11} - 14q^{12} - 6q^{13} - 2q^{14} - 4q^{15} + 504q^{16} - 4q^{17} - 12q^{18} - 6q^{19} - 8q^{20} - 10q^{21} + 8q^{22} + 6q^{23} - 2q^{24} + 511q^{25} + 36q^{26} - 4q^{27} - 16q^{28} - 6q^{29} - 20q^{30} - 10q^{31} - 12q^{32} - 2q^{33} + 4q^{34} + 2q^{35} + 494q^{36} - 2q^{37} + 4q^{38} + 20q^{39} + 30q^{40} + 2q^{41} - 4q^{42} - 22q^{43} - 18q^{44} - 22q^{45} - 26q^{46} - 44q^{48} + 483q^{49} + 20q^{50} - 8q^{51} - 20q^{52} + 6q^{53} + 16q^{54} - 22q^{55} + 30q^{56} + 8q^{57} + 8q^{58} - 12q^{59} - 50q^{60} - 6q^{61} + 8q^{62} - 30q^{63} + 528q^{64} + 46q^{65} + 26q^{66} - 48q^{67} + 14q^{68} - 24q^{70} - 14q^{71} - 46q^{72} - 10q^{73} - 54q^{75} + 10q^{76} - 16q^{77} - 42q^{78} - 12q^{79} - 26q^{80} + 479q^{81} + 14q^{82} - 6q^{83} - 96q^{84} + 16q^{85} - 2q^{86} - 14q^{87} - 46q^{88} + 16q^{89} + 44q^{90} - 8q^{91} + 64q^{92} + 28q^{93} + 50q^{94} + 12q^{95} + 4q^{96} + 12q^{97} - 30q^{98} - 42q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6043))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 6043
6043.2.a.a \(1\) \(48.254\) \(\Q\) None \(-1\) \(-2\) \(0\) \(-2\) \(-\) \(q-q^{2}-2q^{3}-q^{4}+2q^{6}-2q^{7}+3q^{8}+\cdots\)
6043.2.a.b \(243\) \(48.254\) None \(-40\) \(-27\) \(-85\) \(-28\) \(+\)
6043.2.a.c \(259\) \(48.254\) None \(39\) \(25\) \(83\) \(26\) \(-\)