Properties

Label 24.8
Level 24
Weight 8
Dimension 43
Nonzero newspaces 3
Newforms 7
Sturm bound 256
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 7 \)
Sturm bound: \(256\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(24))\).

Total New Old
Modular forms 124 47 77
Cusp forms 100 43 57
Eisenstein series 24 4 20

Trace form

\( 43q - 14q^{2} + 25q^{3} - 236q^{4} - 446q^{5} - 14q^{6} + 3052q^{7} - 428q^{8} - 8021q^{9} + O(q^{10}) \) \( 43q - 14q^{2} + 25q^{3} - 236q^{4} - 446q^{5} - 14q^{6} + 3052q^{7} - 428q^{8} - 8021q^{9} - 284q^{10} + 3028q^{11} - 5144q^{12} + 5154q^{13} + 4636q^{14} - 24138q^{15} - 58208q^{16} + 35626q^{17} + 406q^{18} + 70768q^{19} + 175096q^{20} - 11664q^{21} - 210976q^{22} - 307680q^{23} - 110348q^{24} + 137921q^{25} + 424984q^{26} + 257725q^{27} + 517168q^{28} - 106902q^{29} - 275292q^{30} - 91940q^{31} - 893944q^{32} - 309628q^{33} + 777004q^{34} - 35616q^{35} + 3388q^{36} + 469002q^{37} - 823816q^{38} + 332586q^{39} - 745016q^{40} + 442714q^{41} + 759060q^{42} + 249280q^{43} + 1275264q^{44} - 325134q^{45} - 1789848q^{46} - 2632248q^{47} + 332920q^{48} - 1087081q^{49} + 324610q^{50} + 264422q^{51} - 517104q^{52} + 455554q^{53} + 65470q^{54} + 8823992q^{55} + 1643704q^{56} - 761944q^{57} - 2993516q^{58} - 2921612q^{59} - 2789712q^{60} - 5417118q^{61} + 5767172q^{62} + 224532q^{63} + 3123952q^{64} + 3499100q^{65} - 3707128q^{66} - 3523448q^{67} - 3735840q^{68} - 2845800q^{69} + 18413048q^{70} + 1543616q^{71} + 3815836q^{72} - 2225746q^{73} - 6468800q^{74} + 6356935q^{75} - 9297656q^{76} + 7828800q^{77} - 6804360q^{78} - 11704484q^{79} + 14369088q^{80} + 15456235q^{81} - 24941852q^{82} - 11429812q^{83} - 14932296q^{84} - 6864252q^{85} + 4738312q^{86} + 16382574q^{87} - 4684432q^{88} + 5133874q^{89} + 10622124q^{90} + 14165376q^{91} + 11004480q^{92} - 10069704q^{93} - 17782296q^{94} - 78332168q^{95} + 9297304q^{96} + 4154870q^{97} + 53030538q^{98} + 16638212q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(24))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
24.8.a \(\chi_{24}(1, \cdot)\) 24.8.a.a 1 1
24.8.a.b 1
24.8.a.c 1
24.8.c \(\chi_{24}(23, \cdot)\) None 0 1
24.8.d \(\chi_{24}(13, \cdot)\) 24.8.d.a 14 1
24.8.f \(\chi_{24}(11, \cdot)\) 24.8.f.a 2 1
24.8.f.b 4
24.8.f.c 20

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)