Properties

Label 22.4.a
Level 22
Weight 4
Character orbit a
Rep. character \(\chi_{22}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 12
Trace bound 3

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 22.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(22))\).

Total New Old
Modular forms 11 3 8
Cusp forms 7 3 4
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\(3q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 11q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 138q^{13} \) \(\mathstrut -\mathstrut 32q^{14} \) \(\mathstrut +\mathstrut 186q^{15} \) \(\mathstrut +\mathstrut 48q^{16} \) \(\mathstrut +\mathstrut 126q^{17} \) \(\mathstrut -\mathstrut 74q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 32q^{20} \) \(\mathstrut -\mathstrut 140q^{21} \) \(\mathstrut +\mathstrut 22q^{22} \) \(\mathstrut -\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 32q^{24} \) \(\mathstrut +\mathstrut 191q^{25} \) \(\mathstrut +\mathstrut 212q^{26} \) \(\mathstrut -\mathstrut 170q^{27} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut +\mathstrut 142q^{29} \) \(\mathstrut -\mathstrut 384q^{30} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 110q^{33} \) \(\mathstrut -\mathstrut 84q^{34} \) \(\mathstrut -\mathstrut 348q^{35} \) \(\mathstrut -\mathstrut 60q^{36} \) \(\mathstrut -\mathstrut 228q^{37} \) \(\mathstrut +\mathstrut 488q^{38} \) \(\mathstrut +\mathstrut 288q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 122q^{41} \) \(\mathstrut +\mathstrut 240q^{42} \) \(\mathstrut +\mathstrut 88q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 494q^{45} \) \(\mathstrut +\mathstrut 784q^{46} \) \(\mathstrut +\mathstrut 568q^{47} \) \(\mathstrut -\mathstrut 32q^{48} \) \(\mathstrut -\mathstrut 669q^{49} \) \(\mathstrut -\mathstrut 846q^{50} \) \(\mathstrut +\mathstrut 884q^{51} \) \(\mathstrut -\mathstrut 552q^{52} \) \(\mathstrut +\mathstrut 786q^{53} \) \(\mathstrut +\mathstrut 128q^{54} \) \(\mathstrut -\mathstrut 396q^{55} \) \(\mathstrut -\mathstrut 128q^{56} \) \(\mathstrut -\mathstrut 176q^{57} \) \(\mathstrut -\mathstrut 764q^{58} \) \(\mathstrut -\mathstrut 870q^{59} \) \(\mathstrut +\mathstrut 744q^{60} \) \(\mathstrut -\mathstrut 458q^{61} \) \(\mathstrut -\mathstrut 640q^{62} \) \(\mathstrut +\mathstrut 656q^{63} \) \(\mathstrut +\mathstrut 192q^{64} \) \(\mathstrut +\mathstrut 716q^{65} \) \(\mathstrut +\mathstrut 264q^{66} \) \(\mathstrut +\mathstrut 330q^{67} \) \(\mathstrut +\mathstrut 504q^{68} \) \(\mathstrut +\mathstrut 554q^{69} \) \(\mathstrut +\mathstrut 816q^{70} \) \(\mathstrut -\mathstrut 1690q^{71} \) \(\mathstrut -\mathstrut 296q^{72} \) \(\mathstrut +\mathstrut 770q^{73} \) \(\mathstrut -\mathstrut 1180q^{74} \) \(\mathstrut -\mathstrut 1484q^{75} \) \(\mathstrut -\mathstrut 48q^{76} \) \(\mathstrut +\mathstrut 132q^{77} \) \(\mathstrut -\mathstrut 640q^{78} \) \(\mathstrut -\mathstrut 508q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut -\mathstrut 501q^{81} \) \(\mathstrut +\mathstrut 1628q^{82} \) \(\mathstrut +\mathstrut 1616q^{83} \) \(\mathstrut -\mathstrut 560q^{84} \) \(\mathstrut +\mathstrut 2568q^{85} \) \(\mathstrut +\mathstrut 264q^{86} \) \(\mathstrut -\mathstrut 392q^{87} \) \(\mathstrut +\mathstrut 88q^{88} \) \(\mathstrut +\mathstrut 824q^{89} \) \(\mathstrut +\mathstrut 1300q^{90} \) \(\mathstrut -\mathstrut 448q^{91} \) \(\mathstrut -\mathstrut 56q^{92} \) \(\mathstrut -\mathstrut 822q^{93} \) \(\mathstrut -\mathstrut 560q^{94} \) \(\mathstrut -\mathstrut 1480q^{95} \) \(\mathstrut +\mathstrut 128q^{96} \) \(\mathstrut -\mathstrut 236q^{97} \) \(\mathstrut +\mathstrut 366q^{98} \) \(\mathstrut +\mathstrut 77q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(22))\) 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
22.4.a.a \(1\) \(1.298\) \(\Q\) None \(-2\) \(-7\) \(-19\) \(14\) \(+\) \(-\) \(q-2q^{2}-7q^{3}+4q^{4}-19q^{5}+14q^{6}+\cdots\)
22.4.a.b \(1\) \(1.298\) \(\Q\) None \(-2\) \(4\) \(14\) \(-8\) \(+\) \(+\) \(q-2q^{2}+4q^{3}+4q^{4}+14q^{5}-8q^{6}+\cdots\)
22.4.a.c \(1\) \(1.298\) \(\Q\) None \(2\) \(1\) \(-3\) \(-10\) \(-\) \(-\) \(q+2q^{2}+q^{3}+4q^{4}-3q^{5}+2q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)