Properties

Label 6007.2.a
Level 6007
Weight 2
Character orbit a
Rep. character \(\chi_{6007}(1,\cdot)\)
Character field \(\Q\)
Dimension 500
Newforms 3
Sturm bound 1001
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6007 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6007.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(1001\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6007))\).

Total New Old
Modular forms 501 501 0
Cusp forms 500 500 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.

\(6007\)Dim.
\(+\)\(237\)
\(-\)\(263\)

Trace form

\(500q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 499q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 500q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(500q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 499q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 500q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 493q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 32q^{24} \) \(\mathstrut +\mathstrut 498q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 14q^{27} \) \(\mathstrut -\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 483q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 10q^{39} \) \(\mathstrut +\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 38q^{44} \) \(\mathstrut -\mathstrut 20q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut -\mathstrut 58q^{48} \) \(\mathstrut +\mathstrut 486q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut -\mathstrut 22q^{53} \) \(\mathstrut -\mathstrut 50q^{54} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 20q^{56} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 12q^{58} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 84q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 22q^{63} \) \(\mathstrut +\mathstrut 455q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut -\mathstrut 64q^{66} \) \(\mathstrut +\mathstrut 20q^{67} \) \(\mathstrut -\mathstrut 22q^{68} \) \(\mathstrut -\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 95q^{72} \) \(\mathstrut -\mathstrut 48q^{74} \) \(\mathstrut -\mathstrut 52q^{75} \) \(\mathstrut +\mathstrut 54q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 80q^{78} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 56q^{80} \) \(\mathstrut +\mathstrut 452q^{81} \) \(\mathstrut +\mathstrut 8q^{82} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 170q^{84} \) \(\mathstrut +\mathstrut 78q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 46q^{87} \) \(\mathstrut -\mathstrut 70q^{88} \) \(\mathstrut -\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 56q^{90} \) \(\mathstrut -\mathstrut 36q^{91} \) \(\mathstrut -\mathstrut 54q^{92} \) \(\mathstrut -\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 52q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 58q^{96} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6007))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 6007
6007.2.a.a \(2\) \(47.966\) \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(1\) \(-6\) \(-\) \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
6007.2.a.b \(237\) \(47.966\) None \(-26\) \(-24\) \(-67\) \(-37\) \(+\)
6007.2.a.c \(261\) \(47.966\) None \(26\) \(25\) \(66\) \(37\) \(-\)