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

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

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

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