Properties

Label 22.3.d
Level 22
Weight 3
Character orbit d
Rep. character \(\chi_{22}(7,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 8
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 22.d (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(22, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 16 8 8
Eisenstein series 16 0 16

Trace form

\(8q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 30q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 20q^{6} \) \(\mathstrut -\mathstrut 30q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 24q^{12} \) \(\mathstrut +\mathstrut 30q^{13} \) \(\mathstrut +\mathstrut 16q^{14} \) \(\mathstrut +\mathstrut 42q^{15} \) \(\mathstrut -\mathstrut 8q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 24q^{22} \) \(\mathstrut -\mathstrut 104q^{23} \) \(\mathstrut -\mathstrut 40q^{24} \) \(\mathstrut -\mathstrut 12q^{25} \) \(\mathstrut -\mathstrut 96q^{26} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut 60q^{30} \) \(\mathstrut +\mathstrut 46q^{31} \) \(\mathstrut -\mathstrut 14q^{33} \) \(\mathstrut +\mathstrut 112q^{34} \) \(\mathstrut +\mathstrut 70q^{35} \) \(\mathstrut -\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 108q^{38} \) \(\mathstrut +\mathstrut 130q^{39} \) \(\mathstrut +\mathstrut 80q^{40} \) \(\mathstrut +\mathstrut 250q^{41} \) \(\mathstrut +\mathstrut 56q^{42} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 136q^{45} \) \(\mathstrut -\mathstrut 160q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 144q^{49} \) \(\mathstrut -\mathstrut 80q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 40q^{52} \) \(\mathstrut -\mathstrut 274q^{53} \) \(\mathstrut -\mathstrut 26q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut -\mathstrut 130q^{57} \) \(\mathstrut +\mathstrut 64q^{58} \) \(\mathstrut +\mathstrut 50q^{59} \) \(\mathstrut +\mathstrut 116q^{60} \) \(\mathstrut +\mathstrut 50q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 136q^{66} \) \(\mathstrut +\mathstrut 112q^{67} \) \(\mathstrut +\mathstrut 60q^{68} \) \(\mathstrut +\mathstrut 76q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 54q^{71} \) \(\mathstrut -\mathstrut 80q^{72} \) \(\mathstrut -\mathstrut 70q^{73} \) \(\mathstrut -\mathstrut 40q^{74} \) \(\mathstrut +\mathstrut 318q^{75} \) \(\mathstrut +\mathstrut 266q^{77} \) \(\mathstrut +\mathstrut 104q^{78} \) \(\mathstrut +\mathstrut 370q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 180q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 150q^{83} \) \(\mathstrut -\mathstrut 120q^{84} \) \(\mathstrut -\mathstrut 330q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 72q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 160q^{90} \) \(\mathstrut -\mathstrut 294q^{91} \) \(\mathstrut -\mathstrut 112q^{92} \) \(\mathstrut -\mathstrut 134q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 330q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 308q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(22, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
22.3.d.a \(8\) \(0.599\) 8.0.64000000.1 None \(0\) \(-2\) \(2\) \(-30\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)