Properties

Label 24.5.b
Level $24$
Weight $5$
Character orbit 24.b
Rep. character $\chi_{24}(19,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(24, [\chi])\).

Total New Old
Modular forms 18 8 10
Cusp forms 14 8 6
Eisenstein series 4 0 4

Trace form

\( 8 q - 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} + 216 q^{9} + O(q^{10}) \) \( 8 q - 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} + 216 q^{9} - 324 q^{10} + 192 q^{11} + 180 q^{12} + 420 q^{14} - 712 q^{16} + 240 q^{17} - 162 q^{18} - 704 q^{19} + 168 q^{20} + 592 q^{22} - 108 q^{24} - 664 q^{25} + 1008 q^{26} - 528 q^{28} + 468 q^{30} + 3624 q^{32} + 2716 q^{34} - 5184 q^{35} + 216 q^{36} - 6360 q^{38} + 408 q^{40} + 720 q^{41} - 2412 q^{42} + 10048 q^{43} - 6720 q^{44} + 2616 q^{46} - 3168 q^{48} - 1240 q^{49} + 5394 q^{50} - 4032 q^{51} + 2448 q^{52} + 486 q^{54} + 7512 q^{56} + 3744 q^{57} - 10740 q^{58} + 13056 q^{59} + 10656 q^{60} - 8724 q^{62} - 17632 q^{64} - 1344 q^{65} - 13680 q^{66} - 6656 q^{67} - 5616 q^{68} + 19800 q^{70} - 4860 q^{72} - 16880 q^{73} + 17400 q^{74} - 1152 q^{75} + 14320 q^{76} + 18720 q^{78} + 28512 q^{80} + 5832 q^{81} - 9740 q^{82} - 24000 q^{83} + 21960 q^{84} - 34344 q^{86} - 19616 q^{88} + 15600 q^{89} - 8748 q^{90} + 1344 q^{91} - 48096 q^{92} + 12120 q^{94} - 21528 q^{96} - 12176 q^{97} + 47778 q^{98} + 5184 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.5.b.a 24.b 8.d $8$ $2.481$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)