Properties

Label 22.6.a
Level 22
Weight 6
Character orbit a
Rep. character \(\chi_{22}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 4
Sturm bound 18
Trace bound 3

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 22.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(18\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(22))\).

Total New Old
Modular forms 17 5 12
Cusp forms 13 5 8
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.

\(2\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(3\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 14q^{5} \) \(\mathstrut +\mathstrut 80q^{6} \) \(\mathstrut -\mathstrut 312q^{7} \) \(\mathstrut +\mathstrut 64q^{8} \) \(\mathstrut +\mathstrut 885q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 14q^{5} \) \(\mathstrut +\mathstrut 80q^{6} \) \(\mathstrut -\mathstrut 312q^{7} \) \(\mathstrut +\mathstrut 64q^{8} \) \(\mathstrut +\mathstrut 885q^{9} \) \(\mathstrut -\mathstrut 296q^{10} \) \(\mathstrut -\mathstrut 121q^{11} \) \(\mathstrut -\mathstrut 320q^{12} \) \(\mathstrut +\mathstrut 982q^{13} \) \(\mathstrut -\mathstrut 704q^{14} \) \(\mathstrut -\mathstrut 3024q^{15} \) \(\mathstrut +\mathstrut 1280q^{16} \) \(\mathstrut -\mathstrut 1110q^{17} \) \(\mathstrut +\mathstrut 3892q^{18} \) \(\mathstrut -\mathstrut 3476q^{19} \) \(\mathstrut -\mathstrut 224q^{20} \) \(\mathstrut +\mathstrut 1864q^{21} \) \(\mathstrut -\mathstrut 484q^{22} \) \(\mathstrut +\mathstrut 328q^{23} \) \(\mathstrut +\mathstrut 1280q^{24} \) \(\mathstrut +\mathstrut 4495q^{25} \) \(\mathstrut -\mathstrut 8200q^{26} \) \(\mathstrut -\mathstrut 584q^{27} \) \(\mathstrut -\mathstrut 4992q^{28} \) \(\mathstrut +\mathstrut 7030q^{29} \) \(\mathstrut +\mathstrut 1920q^{30} \) \(\mathstrut +\mathstrut 11776q^{31} \) \(\mathstrut +\mathstrut 1024q^{32} \) \(\mathstrut -\mathstrut 9680q^{33} \) \(\mathstrut -\mathstrut 6360q^{34} \) \(\mathstrut +\mathstrut 35520q^{35} \) \(\mathstrut +\mathstrut 14160q^{36} \) \(\mathstrut -\mathstrut 24566q^{37} \) \(\mathstrut -\mathstrut 8176q^{38} \) \(\mathstrut -\mathstrut 33192q^{39} \) \(\mathstrut -\mathstrut 4736q^{40} \) \(\mathstrut -\mathstrut 8758q^{41} \) \(\mathstrut +\mathstrut 25248q^{42} \) \(\mathstrut +\mathstrut 22292q^{43} \) \(\mathstrut -\mathstrut 1936q^{44} \) \(\mathstrut -\mathstrut 49802q^{45} \) \(\mathstrut -\mathstrut 14048q^{46} \) \(\mathstrut -\mathstrut 7736q^{47} \) \(\mathstrut -\mathstrut 5120q^{48} \) \(\mathstrut +\mathstrut 20397q^{49} \) \(\mathstrut -\mathstrut 5316q^{50} \) \(\mathstrut +\mathstrut 57992q^{51} \) \(\mathstrut +\mathstrut 15712q^{52} \) \(\mathstrut -\mathstrut 11826q^{53} \) \(\mathstrut -\mathstrut 6016q^{54} \) \(\mathstrut +\mathstrut 13794q^{55} \) \(\mathstrut -\mathstrut 11264q^{56} \) \(\mathstrut +\mathstrut 15520q^{57} \) \(\mathstrut +\mathstrut 16792q^{58} \) \(\mathstrut +\mathstrut 44436q^{59} \) \(\mathstrut -\mathstrut 48384q^{60} \) \(\mathstrut -\mathstrut 2314q^{61} \) \(\mathstrut +\mathstrut 59648q^{62} \) \(\mathstrut -\mathstrut 149272q^{63} \) \(\mathstrut +\mathstrut 20480q^{64} \) \(\mathstrut +\mathstrut 52004q^{65} \) \(\mathstrut -\mathstrut 17424q^{66} \) \(\mathstrut +\mathstrut 26380q^{67} \) \(\mathstrut -\mathstrut 17760q^{68} \) \(\mathstrut -\mathstrut 20884q^{69} \) \(\mathstrut +\mathstrut 10848q^{70} \) \(\mathstrut -\mathstrut 11656q^{71} \) \(\mathstrut +\mathstrut 62272q^{72} \) \(\mathstrut -\mathstrut 169782q^{73} \) \(\mathstrut +\mathstrut 128792q^{74} \) \(\mathstrut +\mathstrut 70180q^{75} \) \(\mathstrut -\mathstrut 55616q^{76} \) \(\mathstrut +\mathstrut 5808q^{77} \) \(\mathstrut +\mathstrut 128q^{78} \) \(\mathstrut -\mathstrut 92640q^{79} \) \(\mathstrut -\mathstrut 3584q^{80} \) \(\mathstrut +\mathstrut 333309q^{81} \) \(\mathstrut -\mathstrut 129400q^{82} \) \(\mathstrut +\mathstrut 91868q^{83} \) \(\mathstrut +\mathstrut 29824q^{84} \) \(\mathstrut -\mathstrut 92220q^{85} \) \(\mathstrut -\mathstrut 167088q^{86} \) \(\mathstrut -\mathstrut 190712q^{87} \) \(\mathstrut -\mathstrut 7744q^{88} \) \(\mathstrut -\mathstrut 24538q^{89} \) \(\mathstrut -\mathstrut 426248q^{90} \) \(\mathstrut -\mathstrut 31568q^{91} \) \(\mathstrut +\mathstrut 5248q^{92} \) \(\mathstrut +\mathstrut 444204q^{93} \) \(\mathstrut +\mathstrut 269344q^{94} \) \(\mathstrut -\mathstrut 125800q^{95} \) \(\mathstrut +\mathstrut 20480q^{96} \) \(\mathstrut -\mathstrut 155002q^{97} \) \(\mathstrut +\mathstrut 53220q^{98} \) \(\mathstrut +\mathstrut 85547q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(22))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11
22.6.a.a \(1\) \(3.528\) \(\Q\) None \(-4\) \(-21\) \(81\) \(98\) \(+\) \(-\) \(q-4q^{2}-21q^{3}+2^{4}q^{4}+3^{4}q^{5}+84q^{6}+\cdots\)
22.6.a.b \(1\) \(3.528\) \(\Q\) None \(-4\) \(1\) \(-51\) \(-166\) \(+\) \(+\) \(q-4q^{2}+q^{3}+2^{4}q^{4}-51q^{5}-4q^{6}+\cdots\)
22.6.a.c \(1\) \(3.528\) \(\Q\) None \(4\) \(-29\) \(-31\) \(-230\) \(-\) \(-\) \(q+4q^{2}-29q^{3}+2^{4}q^{4}-31q^{5}-116q^{6}+\cdots\)
22.6.a.d \(2\) \(3.528\) \(\Q(\sqrt{793}) \) None \(8\) \(29\) \(-13\) \(-14\) \(-\) \(+\) \(q+4q^{2}+(15-\beta )q^{3}+2^{4}q^{4}+(-9+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)