Properties

Label 6043.2.a
Level 6043
Weight 2
Character orbit a
Rep. character \(\chi_{6043}(1,\cdot)\)
Character field \(\Q\)
Dimension 503
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6043))\) into irreducible Hecke orbits

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 \(39\) \(25\) \(83\) \(26\) \(-\)