Properties

Label 6.12.a
Level 6
Weight 12
Character orbit a
Rep. character \(\chi_{6}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 12
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 6.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(6))\).

Total New Old
Modular forms 13 3 10
Cusp forms 9 3 6
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\( 3q - 32q^{2} + 243q^{3} + 3072q^{4} - 2334q^{5} + 7776q^{6} + 55392q^{7} - 32768q^{8} + 177147q^{9} + O(q^{10}) \) \( 3q - 32q^{2} + 243q^{3} + 3072q^{4} - 2334q^{5} + 7776q^{6} + 55392q^{7} - 32768q^{8} + 177147q^{9} + 307008q^{10} - 1699116q^{11} + 248832q^{12} + 217266q^{13} + 335360q^{14} - 3369438q^{15} + 3145728q^{16} + 8603622q^{17} - 1889568q^{18} + 7200204q^{19} - 2390016q^{20} - 21757248q^{21} + 5811840q^{22} - 1057800q^{23} + 7962624q^{24} + 37532181q^{25} - 165855424q^{26} + 14348907q^{27} + 56721408q^{28} + 70389066q^{29} + 164275776q^{30} - 146569368q^{31} - 33554432q^{32} - 214136460q^{33} + 255268800q^{34} + 1123978944q^{35} + 181398528q^{36} - 1480918566q^{37} - 925913728q^{38} - 611837550q^{39} + 314376192q^{40} + 899560158q^{41} + 1208452608q^{42} - 273486252q^{43} - 1739894784q^{44} - 137820366q^{45} + 1348363008q^{46} + 1552169280q^{47} + 254803968q^{48} + 2904631227q^{49} - 3482708192q^{50} - 544856058q^{51} + 222480384q^{52} - 1324585278q^{53} + 459165024q^{54} + 1121307192q^{55} + 343408640q^{56} - 5621075028q^{57} - 408318912q^{58} + 4411180500q^{59} - 3450304512q^{60} - 12529017966q^{61} + 14322308864q^{62} + 3270842208q^{63} + 3221225472q^{64} - 16758434292q^{65} - 4947682176q^{66} + 27115273932q^{67} + 8810108928q^{68} + 25109273592q^{69} - 28315634688q^{70} - 25932460536q^{71} - 1934917632q^{72} + 6082420686q^{73} + 26916324416q^{74} + 16692865317q^{75} + 7373008896q^{76} - 28048880640q^{77} - 19034606016q^{78} - 58308979368q^{79} - 2447376384q^{80} + 10460353203q^{81} - 52338500928q^{82} + 37956458316q^{83} - 22279421952q^{84} + 121299146244q^{85} + 48461612672q^{86} - 40525895862q^{87} + 5951324160q^{88} - 210662658q^{89} + 18128515392q^{90} - 49315648704q^{91} - 1083187200q^{92} - 7597286136q^{93} + 127169639424q^{94} + 13965964680q^{95} + 8153726976q^{96} - 49488374586q^{97} - 150071184672q^{98} - 100331100684q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(6))\) 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
6.12.a.a \(1\) \(4.610\) \(\Q\) None \(-32\) \(-243\) \(5766\) \(72464\) \(+\) \(+\) \(q-2^{5}q^{2}-3^{5}q^{3}+2^{10}q^{4}+5766q^{5}+\cdots\)
6.12.a.b \(1\) \(4.610\) \(\Q\) None \(-32\) \(243\) \(-11730\) \(-50008\) \(+\) \(-\) \(q-2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}-11730q^{5}+\cdots\)
6.12.a.c \(1\) \(4.610\) \(\Q\) None \(32\) \(243\) \(3630\) \(32936\) \(-\) \(-\) \(q+2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+3630q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)