Properties

Label 4021.2.a
Level 4021
Weight 2
Character orbit a
Rep. character \(\chi_{4021}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newform subspaces 3
Sturm bound 670
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4021.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(670\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4021))\).

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.

\(4021\)Dim.
\(+\)\(152\)
\(-\)\(182\)

Trace form

\( 334q + 330q^{4} - 2q^{5} - 2q^{6} + 6q^{8} + 334q^{9} + O(q^{10}) \) \( 334q + 330q^{4} - 2q^{5} - 2q^{6} + 6q^{8} + 334q^{9} - 6q^{10} + 10q^{11} + 2q^{12} - 12q^{13} + 6q^{14} - 6q^{15} + 326q^{16} - 8q^{17} - 8q^{18} - 6q^{19} - 2q^{20} - 24q^{21} + 16q^{22} + 2q^{23} + 2q^{24} + 336q^{25} + 8q^{26} + 6q^{27} - 4q^{28} - 4q^{29} + 2q^{31} + 22q^{32} + 6q^{33} - 8q^{34} + 14q^{35} + 354q^{36} - 4q^{37} - 12q^{38} - 8q^{39} - 50q^{40} + 8q^{41} + 28q^{42} - 2q^{43} + 46q^{44} - 4q^{45} - 28q^{46} - 2q^{47} - 10q^{48} + 328q^{49} + 6q^{50} + 8q^{51} - 42q^{52} - 8q^{53} + 14q^{54} - 6q^{55} + 32q^{56} - 22q^{57} - 28q^{58} + 40q^{59} - 64q^{60} - 42q^{61} - 16q^{62} - 38q^{63} + 314q^{64} - 34q^{65} - 6q^{66} - 10q^{67} - 26q^{68} - 32q^{69} - 14q^{70} - 8q^{71} - 2q^{72} - 22q^{74} - 42q^{75} - 60q^{76} - 6q^{77} - 52q^{78} + 16q^{79} - 36q^{80} + 310q^{81} - 36q^{82} + 18q^{83} - 136q^{84} + 6q^{85} - 34q^{86} - 24q^{87} - 10q^{88} - 38q^{89} - 130q^{90} - 16q^{91} - 36q^{94} + 10q^{95} - 14q^{96} + 6q^{97} - 8q^{98} + 100q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4021))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 4021
4021.2.a.a \(1\) \(32.108\) \(\Q\) None \(-2\) \(1\) \(3\) \(4\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
4021.2.a.b \(151\) \(32.108\) None \(-16\) \(-29\) \(-27\) \(-18\) \(+\)
4021.2.a.c \(182\) \(32.108\) None \(18\) \(28\) \(22\) \(14\) \(-\)