Properties

Label 4007.2.a
Level 4007
Weight 2
Character orbit a
Rep. character \(\chi_{4007}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4007))\) into newform subspaces

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 \(14\) \(22\) \(14\) \(48\) \(-\)