Properties

Label 4001.2.a
Level 4001
Weight 2
Character orbit a
Rep. character \(\chi_{4001}(1,\cdot)\)
Character field \(\Q\)
Dimension 333
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4001))\) into irreducible Hecke orbits

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 \(3\) \(28\) \(15\) \(49\) \(-\)