Properties

Label 24.3.b
Level $24$
Weight $3$
Character orbit 24.b
Rep. character $\chi_{24}(19,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

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

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