Properties

Label 24.3.b
Level 24
Weight 3
Character orbit b
Rep. character \(\chi_{24}(19,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 24.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(24, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\(4q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 36q^{14} \) \(\mathstrut -\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 32q^{19} \) \(\mathstrut +\mathstrut 72q^{20} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut -\mathstrut 44q^{25} \) \(\mathstrut -\mathstrut 96q^{26} \) \(\mathstrut -\mathstrut 48q^{28} \) \(\mathstrut -\mathstrut 60q^{30} \) \(\mathstrut -\mathstrut 88q^{32} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut -\mathstrut 24q^{36} \) \(\mathstrut +\mathstrut 40q^{38} \) \(\mathstrut +\mathstrut 120q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 84q^{42} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 64q^{44} \) \(\mathstrut -\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 96q^{48} \) \(\mathstrut -\mathstrut 44q^{49} \) \(\mathstrut -\mathstrut 118q^{50} \) \(\mathstrut -\mathstrut 96q^{51} \) \(\mathstrut -\mathstrut 48q^{52} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 168q^{56} \) \(\mathstrut -\mathstrut 48q^{57} \) \(\mathstrut +\mathstrut 156q^{58} \) \(\mathstrut -\mathstrut 128q^{59} \) \(\mathstrut -\mathstrut 96q^{60} \) \(\mathstrut +\mathstrut 204q^{62} \) \(\mathstrut -\mathstrut 32q^{64} \) \(\mathstrut +\mathstrut 96q^{65} \) \(\mathstrut +\mathstrut 48q^{66} \) \(\mathstrut -\mathstrut 256q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut +\mathstrut 200q^{73} \) \(\mathstrut -\mathstrut 120q^{74} \) \(\mathstrut +\mathstrut 192q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 48q^{78} \) \(\mathstrut -\mathstrut 96q^{80} \) \(\mathstrut +\mathstrut 36q^{81} \) \(\mathstrut -\mathstrut 124q^{82} \) \(\mathstrut +\mathstrut 160q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut +\mathstrut 88q^{86} \) \(\mathstrut +\mathstrut 32q^{88} \) \(\mathstrut -\mathstrut 200q^{89} \) \(\mathstrut +\mathstrut 36q^{90} \) \(\mathstrut +\mathstrut 288q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut -\mathstrut 168q^{94} \) \(\mathstrut -\mathstrut 24q^{96} \) \(\mathstrut +\mathstrut 56q^{97} \) \(\mathstrut +\mathstrut 170q^{98} \) \(\mathstrut -\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.3.b.a \(4\) \(0.654\) 4.0.4752.1 None \(2\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)