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Properties

Label 24.7.b
Level $24$
Weight $7$
Character orbit 24.b
Rep. character $\chi_{24}(19,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(24, [\chi])\).

Total New Old
Modular forms 26 12 14
Cusp forms 22 12 10
Eisenstein series 4 0 4

Trace form

\( 12 q + 10 q^{2} + 24 q^{4} + 162 q^{6} + 796 q^{8} + 2916 q^{9} + O(q^{10}) \) \( 12 q + 10 q^{2} + 24 q^{4} + 162 q^{6} + 796 q^{8} + 2916 q^{9} + 2172 q^{10} + 2720 q^{11} - 972 q^{12} - 6444 q^{14} + 11640 q^{16} - 4888 q^{17} + 2430 q^{18} + 3936 q^{19} - 31608 q^{20} - 60432 q^{22} + 26244 q^{24} - 27204 q^{25} + 53952 q^{26} - 57072 q^{28} - 24300 q^{30} + 109480 q^{32} + 47388 q^{34} + 162336 q^{35} + 5832 q^{36} - 89080 q^{38} + 72120 q^{40} - 54280 q^{41} + 21060 q^{42} - 49824 q^{43} + 229184 q^{44} + 171864 q^{46} - 23328 q^{48} - 304644 q^{49} - 500078 q^{50} + 80352 q^{51} + 256848 q^{52} + 39366 q^{54} - 699816 q^{56} - 136080 q^{57} - 409524 q^{58} - 886144 q^{59} + 95904 q^{60} + 691356 q^{62} - 500640 q^{64} + 473376 q^{65} + 3888 q^{66} + 1565952 q^{67} + 669104 q^{68} + 473784 q^{70} + 193428 q^{72} + 555480 q^{73} - 753720 q^{74} - 1073088 q^{75} - 293136 q^{76} - 535248 q^{78} - 251616 q^{80} + 708588 q^{81} + 2317716 q^{82} + 2497760 q^{83} - 1168344 q^{84} + 476024 q^{86} + 971424 q^{88} + 367400 q^{89} + 527796 q^{90} - 4475808 q^{91} - 377376 q^{92} - 2642568 q^{94} + 2372328 q^{96} - 1165656 q^{97} + 182674 q^{98} + 660960 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.7.b.a 24.b 8.d $12$ $5.521$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{2}-\beta _{2}q^{3}+(2+\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)