Properties

Label 4022.2.a
Level 4022
Weight 2
Character orbit a
Rep. character \(\chi_{4022}(1,\cdot)\)
Character field \(\Q\)
Dimension 168
Newforms 6
Sturm bound 1006
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4022 = 2 \cdot 2011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4022.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(1006\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4022))\).

Total New Old
Modular forms 505 168 337
Cusp forms 502 168 334
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(2011\)FrickeDim.
\(+\)\(+\)\(+\)\(37\)
\(+\)\(-\)\(-\)\(47\)
\(-\)\(+\)\(-\)\(50\)
\(-\)\(-\)\(+\)\(34\)
Plus space\(+\)\(71\)
Minus space\(-\)\(97\)

Trace form

\(168q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 168q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 174q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(168q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 168q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 174q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 168q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 170q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 28q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 20q^{33} \) \(\mathstrut -\mathstrut 12q^{34} \) \(\mathstrut +\mathstrut 32q^{35} \) \(\mathstrut +\mathstrut 174q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 26q^{43} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut +\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 176q^{49} \) \(\mathstrut -\mathstrut 16q^{50} \) \(\mathstrut +\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 4q^{54} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut +\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 40q^{63} \) \(\mathstrut +\mathstrut 168q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 40q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 40q^{75} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut -\mathstrut 16q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 144q^{81} \) \(\mathstrut +\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut +\mathstrut 60q^{91} \) \(\mathstrut -\mathstrut 4q^{92} \) \(\mathstrut -\mathstrut 40q^{93} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4022))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 2011
4022.2.a.a \(1\) \(32.116\) \(\Q\) None \(-1\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
4022.2.a.b \(3\) \(32.116\) 3.3.169.1 None \(3\) \(-3\) \(1\) \(-1\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
4022.2.a.c \(31\) \(32.116\) None \(31\) \(-14\) \(-13\) \(-29\) \(-\) \(-\)
4022.2.a.d \(37\) \(32.116\) None \(-37\) \(-5\) \(-13\) \(-22\) \(+\) \(+\)
4022.2.a.e \(46\) \(32.116\) None \(-46\) \(8\) \(14\) \(28\) \(+\) \(-\)
4022.2.a.f \(50\) \(32.116\) None \(50\) \(18\) \(11\) \(30\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2011))\)\(^{\oplus 2}\)