Properties

Label 4007.2.a
Level 4007
Weight 2
Character orbit a
Rep. character \(\chi_{4007}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newforms 2
Sturm bound 668
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4007 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4007.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(668\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4007))\).

Total New Old
Modular forms 335 335 0
Cusp forms 334 334 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.

\(4007\)Dim.
\(+\)\(139\)
\(-\)\(195\)

Trace form

\(334q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 333q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 332q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(334q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 333q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 332q^{9} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 343q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 28q^{22} \) \(\mathstrut +\mathstrut 6q^{24} \) \(\mathstrut +\mathstrut 346q^{25} \) \(\mathstrut +\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut 6q^{27} \) \(\mathstrut +\mathstrut 18q^{28} \) \(\mathstrut +\mathstrut 22q^{30} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut -\mathstrut 13q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 307q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 24q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 42q^{42} \) \(\mathstrut +\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 22q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 32q^{48} \) \(\mathstrut +\mathstrut 328q^{49} \) \(\mathstrut +\mathstrut 13q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 34q^{57} \) \(\mathstrut +\mathstrut 26q^{58} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 68q^{60} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 357q^{64} \) \(\mathstrut +\mathstrut 42q^{65} \) \(\mathstrut -\mathstrut 64q^{66} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut -\mathstrut 10q^{68} \) \(\mathstrut -\mathstrut 52q^{69} \) \(\mathstrut -\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 2q^{71} \) \(\mathstrut -\mathstrut 31q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 52q^{75} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 326q^{81} \) \(\mathstrut -\mathstrut 8q^{82} \) \(\mathstrut -\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 22q^{85} \) \(\mathstrut +\mathstrut 4q^{86} \) \(\mathstrut +\mathstrut 40q^{87} \) \(\mathstrut +\mathstrut 88q^{88} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 64q^{90} \) \(\mathstrut +\mathstrut 20q^{91} \) \(\mathstrut +\mathstrut 2q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 24q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut 21q^{98} \) \(\mathstrut -\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4007))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 4007
4007.2.a.a \(139\) \(31.996\) None \(-13\) \(-22\) \(-16\) \(-44\) \(+\)
4007.2.a.b \(195\) \(31.996\) None \(14\) \(22\) \(14\) \(48\) \(-\)