Properties

Label 6.4.a
Level 6
Weight 4
Character orbit a
Rep. character \(\chi_{6}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 6.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(6))\).

Total New Old
Modular forms 5 1 4
Cusp forms 1 1 0
Eisenstein series 4 0 4

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

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 38q^{13} \) \(\mathstrut +\mathstrut 32q^{14} \) \(\mathstrut -\mathstrut 18q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 126q^{17} \) \(\mathstrut -\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut +\mathstrut 24q^{20} \) \(\mathstrut +\mathstrut 48q^{21} \) \(\mathstrut -\mathstrut 24q^{22} \) \(\mathstrut +\mathstrut 168q^{23} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 89q^{25} \) \(\mathstrut -\mathstrut 76q^{26} \) \(\mathstrut -\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut +\mathstrut 30q^{29} \) \(\mathstrut +\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 88q^{31} \) \(\mathstrut -\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 36q^{33} \) \(\mathstrut +\mathstrut 252q^{34} \) \(\mathstrut -\mathstrut 96q^{35} \) \(\mathstrut +\mathstrut 36q^{36} \) \(\mathstrut +\mathstrut 254q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 114q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 96q^{42} \) \(\mathstrut -\mathstrut 52q^{43} \) \(\mathstrut +\mathstrut 48q^{44} \) \(\mathstrut +\mathstrut 54q^{45} \) \(\mathstrut -\mathstrut 336q^{46} \) \(\mathstrut -\mathstrut 96q^{47} \) \(\mathstrut -\mathstrut 48q^{48} \) \(\mathstrut -\mathstrut 87q^{49} \) \(\mathstrut +\mathstrut 178q^{50} \) \(\mathstrut +\mathstrut 378q^{51} \) \(\mathstrut +\mathstrut 152q^{52} \) \(\mathstrut +\mathstrut 198q^{53} \) \(\mathstrut +\mathstrut 54q^{54} \) \(\mathstrut +\mathstrut 72q^{55} \) \(\mathstrut +\mathstrut 128q^{56} \) \(\mathstrut -\mathstrut 60q^{57} \) \(\mathstrut -\mathstrut 60q^{58} \) \(\mathstrut -\mathstrut 660q^{59} \) \(\mathstrut -\mathstrut 72q^{60} \) \(\mathstrut -\mathstrut 538q^{61} \) \(\mathstrut +\mathstrut 176q^{62} \) \(\mathstrut -\mathstrut 144q^{63} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut +\mathstrut 228q^{65} \) \(\mathstrut +\mathstrut 72q^{66} \) \(\mathstrut +\mathstrut 884q^{67} \) \(\mathstrut -\mathstrut 504q^{68} \) \(\mathstrut -\mathstrut 504q^{69} \) \(\mathstrut +\mathstrut 192q^{70} \) \(\mathstrut +\mathstrut 792q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 218q^{73} \) \(\mathstrut -\mathstrut 508q^{74} \) \(\mathstrut +\mathstrut 267q^{75} \) \(\mathstrut +\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 192q^{77} \) \(\mathstrut +\mathstrut 228q^{78} \) \(\mathstrut -\mathstrut 520q^{79} \) \(\mathstrut +\mathstrut 96q^{80} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 84q^{82} \) \(\mathstrut -\mathstrut 492q^{83} \) \(\mathstrut +\mathstrut 192q^{84} \) \(\mathstrut -\mathstrut 756q^{85} \) \(\mathstrut +\mathstrut 104q^{86} \) \(\mathstrut -\mathstrut 90q^{87} \) \(\mathstrut -\mathstrut 96q^{88} \) \(\mathstrut +\mathstrut 810q^{89} \) \(\mathstrut -\mathstrut 108q^{90} \) \(\mathstrut -\mathstrut 608q^{91} \) \(\mathstrut +\mathstrut 672q^{92} \) \(\mathstrut +\mathstrut 264q^{93} \) \(\mathstrut +\mathstrut 192q^{94} \) \(\mathstrut +\mathstrut 120q^{95} \) \(\mathstrut +\mathstrut 96q^{96} \) \(\mathstrut +\mathstrut 1154q^{97} \) \(\mathstrut +\mathstrut 174q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
6.4.a.a \(1\) \(0.354\) \(\Q\) None \(-2\) \(-3\) \(6\) \(-16\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)