Properties

Label 22.4.c
Level 22
Weight 4
Character orbit c
Rep. character \(\chi_{22}(3,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 12
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 22.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(22, [\chi])\).

Total New Old
Modular forms 44 12 32
Cusp forms 28 12 16
Eisenstein series 16 0 16

Trace form

\(12q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 42q^{6} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 145q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 42q^{6} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 145q^{9} \) \(\mathstrut -\mathstrut 104q^{10} \) \(\mathstrut -\mathstrut 111q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 98q^{13} \) \(\mathstrut +\mathstrut 52q^{14} \) \(\mathstrut +\mathstrut 224q^{15} \) \(\mathstrut -\mathstrut 48q^{16} \) \(\mathstrut +\mathstrut 184q^{17} \) \(\mathstrut +\mathstrut 304q^{18} \) \(\mathstrut -\mathstrut 213q^{19} \) \(\mathstrut +\mathstrut 32q^{20} \) \(\mathstrut -\mathstrut 280q^{21} \) \(\mathstrut -\mathstrut 22q^{22} \) \(\mathstrut +\mathstrut 404q^{23} \) \(\mathstrut +\mathstrut 168q^{24} \) \(\mathstrut +\mathstrut 109q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut +\mathstrut 245q^{27} \) \(\mathstrut -\mathstrut 104q^{28} \) \(\mathstrut -\mathstrut 392q^{29} \) \(\mathstrut -\mathstrut 396q^{30} \) \(\mathstrut +\mathstrut 96q^{31} \) \(\mathstrut -\mathstrut 128q^{32} \) \(\mathstrut -\mathstrut 1155q^{33} \) \(\mathstrut -\mathstrut 516q^{34} \) \(\mathstrut -\mathstrut 662q^{35} \) \(\mathstrut -\mathstrut 40q^{36} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 548q^{38} \) \(\mathstrut -\mathstrut 448q^{39} \) \(\mathstrut +\mathstrut 224q^{40} \) \(\mathstrut +\mathstrut 708q^{41} \) \(\mathstrut +\mathstrut 1940q^{42} \) \(\mathstrut +\mathstrut 2602q^{43} \) \(\mathstrut +\mathstrut 1016q^{44} \) \(\mathstrut +\mathstrut 2404q^{45} \) \(\mathstrut -\mathstrut 424q^{46} \) \(\mathstrut -\mathstrut 818q^{47} \) \(\mathstrut +\mathstrut 32q^{48} \) \(\mathstrut -\mathstrut 661q^{49} \) \(\mathstrut +\mathstrut 166q^{50} \) \(\mathstrut -\mathstrut 1579q^{51} \) \(\mathstrut -\mathstrut 408q^{52} \) \(\mathstrut -\mathstrut 526q^{53} \) \(\mathstrut -\mathstrut 2288q^{54} \) \(\mathstrut +\mathstrut 26q^{55} \) \(\mathstrut +\mathstrut 128q^{56} \) \(\mathstrut -\mathstrut 769q^{57} \) \(\mathstrut -\mathstrut 916q^{58} \) \(\mathstrut -\mathstrut 955q^{59} \) \(\mathstrut -\mathstrut 1224q^{60} \) \(\mathstrut +\mathstrut 718q^{61} \) \(\mathstrut +\mathstrut 2020q^{62} \) \(\mathstrut +\mathstrut 1064q^{63} \) \(\mathstrut -\mathstrut 192q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut +\mathstrut 2656q^{66} \) \(\mathstrut +\mathstrut 490q^{67} \) \(\mathstrut +\mathstrut 736q^{68} \) \(\mathstrut -\mathstrut 554q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 1550q^{71} \) \(\mathstrut -\mathstrut 824q^{72} \) \(\mathstrut -\mathstrut 1640q^{73} \) \(\mathstrut -\mathstrut 220q^{74} \) \(\mathstrut -\mathstrut 3561q^{75} \) \(\mathstrut -\mathstrut 712q^{76} \) \(\mathstrut +\mathstrut 498q^{77} \) \(\mathstrut -\mathstrut 2320q^{78} \) \(\mathstrut +\mathstrut 748q^{79} \) \(\mathstrut -\mathstrut 512q^{80} \) \(\mathstrut +\mathstrut 3006q^{81} \) \(\mathstrut +\mathstrut 62q^{82} \) \(\mathstrut +\mathstrut 2829q^{83} \) \(\mathstrut +\mathstrut 2400q^{84} \) \(\mathstrut -\mathstrut 148q^{85} \) \(\mathstrut +\mathstrut 2186q^{86} \) \(\mathstrut +\mathstrut 3792q^{87} \) \(\mathstrut +\mathstrut 472q^{88} \) \(\mathstrut -\mathstrut 474q^{89} \) \(\mathstrut +\mathstrut 1640q^{90} \) \(\mathstrut +\mathstrut 4278q^{91} \) \(\mathstrut -\mathstrut 1624q^{92} \) \(\mathstrut +\mathstrut 7052q^{93} \) \(\mathstrut -\mathstrut 1040q^{94} \) \(\mathstrut -\mathstrut 720q^{95} \) \(\mathstrut -\mathstrut 128q^{96} \) \(\mathstrut -\mathstrut 3109q^{97} \) \(\mathstrut -\mathstrut 4776q^{98} \) \(\mathstrut -\mathstrut 7867q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(22, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
22.4.c.a \(4\) \(1.298\) \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(3\) \(25\) \(q-2\zeta_{10}q^{2}+(-3+3\zeta_{10}+8\zeta_{10}^{3})q^{3}+\cdots\)
22.4.c.b \(8\) \(1.298\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(3\) \(5\) \(-1\) \(q-2\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)