Properties

Label 4001.2.a
Level 4001
Weight 2
Character orbit a
Rep. character \(\chi_{4001}(1,\cdot)\)
Character field \(\Q\)
Dimension 333
Newform subspaces 2
Sturm bound 667
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4001.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(667\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4001))\).

Total New Old
Modular forms 334 334 0
Cusp forms 333 333 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.

\(4001\)Dim.
\(+\)\(149\)
\(-\)\(184\)

Trace form

\( 333q - 3q^{2} + 333q^{4} - 4q^{5} + 2q^{7} - 9q^{8} + 325q^{9} + O(q^{10}) \) \( 333q - 3q^{2} + 333q^{4} - 4q^{5} + 2q^{7} - 9q^{8} + 325q^{9} - 2q^{10} - 6q^{11} - 2q^{13} - 16q^{14} - 6q^{15} + 337q^{16} - 10q^{17} - 25q^{18} - 26q^{20} - 8q^{21} - 2q^{22} - 8q^{23} - 18q^{24} + 333q^{25} - 6q^{26} - 6q^{27} - 2q^{28} - 24q^{29} - 32q^{30} + 20q^{31} - 21q^{32} - 16q^{33} - 2q^{34} - 20q^{35} + 323q^{36} - 6q^{39} - 16q^{40} - 16q^{41} + 10q^{42} + 10q^{43} - 22q^{44} - 14q^{45} + 6q^{46} + 28q^{48} + 327q^{49} + 17q^{50} - 38q^{51} + 10q^{52} - 2q^{53} + 10q^{54} + 8q^{55} - 20q^{56} - 6q^{58} + 2q^{59} - 12q^{60} - 8q^{61} + 4q^{62} - 32q^{63} + 323q^{64} - 46q^{65} + 24q^{66} - 20q^{67} + 22q^{69} - 60q^{70} - 6q^{71} - 15q^{72} - 2q^{73} - 18q^{74} + 4q^{75} - 44q^{76} + 6q^{77} + 48q^{78} + 14q^{79} - 8q^{80} + 285q^{81} - 34q^{82} - 2q^{83} - 30q^{85} + 28q^{86} - 16q^{87} - 28q^{88} - 22q^{89} + 54q^{90} + 16q^{91} + 22q^{92} + 60q^{93} + 10q^{94} - 46q^{95} - 8q^{96} - 2q^{97} - 29q^{98} - 78q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4001))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 4001
4001.2.a.a \(149\) \(31.948\) None \(-6\) \(-28\) \(-19\) \(-47\) \(+\)
4001.2.a.b \(184\) \(31.948\) None \(3\) \(28\) \(15\) \(49\) \(-\)