Properties

Label 6029.2.a
Level 6029
Weight 2
Character orbit a
Rep. character \(\chi_{6029}(1,\cdot)\)
Character field \(\Q\)
Dimension 502
Newforms 2
Sturm bound 1005
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6029 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6029.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(1005\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6029))\).

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.

\(6029\)Dim.
\(+\)\(234\)
\(-\)\(268\)

Trace form

\(502q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 502q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 498q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(502q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 502q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 498q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 498q^{16} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 22q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 484q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 22q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 20q^{34} \) \(\mathstrut -\mathstrut 14q^{35} \) \(\mathstrut +\mathstrut 472q^{36} \) \(\mathstrut +\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 42q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 14q^{47} \) \(\mathstrut -\mathstrut 24q^{48} \) \(\mathstrut +\mathstrut 504q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 24q^{52} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 40q^{55} \) \(\mathstrut -\mathstrut 46q^{56} \) \(\mathstrut +\mathstrut 30q^{57} \) \(\mathstrut -\mathstrut 32q^{58} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 30q^{60} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 20q^{62} \) \(\mathstrut +\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 476q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 104q^{66} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 44q^{68} \) \(\mathstrut -\mathstrut 14q^{69} \) \(\mathstrut -\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 36q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 88q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 72q^{80} \) \(\mathstrut +\mathstrut 478q^{81} \) \(\mathstrut +\mathstrut 38q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 28q^{86} \) \(\mathstrut +\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 16q^{88} \) \(\mathstrut -\mathstrut 14q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 6q^{93} \) \(\mathstrut +\mathstrut 32q^{94} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 28q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6029))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 6029
6029.2.a.a \(234\) \(48.142\) None \(-10\) \(-43\) \(-24\) \(-61\) \(+\)
6029.2.a.b \(268\) \(48.142\) None \(8\) \(43\) \(18\) \(59\) \(-\)