Properties

Label 24.5
Level 24
Weight 5
Dimension 26
Nonzero newspaces 3
Newforms 5
Sturm bound 160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 5 \)
Sturm bound: \(160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(24))\).

Total New Old
Modular forms 76 30 46
Cusp forms 52 26 26
Eisenstein series 24 4 20

Trace form

\(26q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 34q^{6} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut -\mathstrut 180q^{8} \) \(\mathstrut +\mathstrut 314q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 34q^{6} \) \(\mathstrut +\mathstrut 20q^{7} \) \(\mathstrut -\mathstrut 180q^{8} \) \(\mathstrut +\mathstrut 314q^{9} \) \(\mathstrut -\mathstrut 332q^{10} \) \(\mathstrut +\mathstrut 192q^{11} \) \(\mathstrut +\mathstrut 160q^{12} \) \(\mathstrut -\mathstrut 248q^{13} \) \(\mathstrut +\mathstrut 420q^{14} \) \(\mathstrut -\mathstrut 708q^{15} \) \(\mathstrut -\mathstrut 864q^{16} \) \(\mathstrut +\mathstrut 240q^{17} \) \(\mathstrut -\mathstrut 394q^{18} \) \(\mathstrut +\mathstrut 120q^{19} \) \(\mathstrut +\mathstrut 168q^{20} \) \(\mathstrut +\mathstrut 1224q^{21} \) \(\mathstrut -\mathstrut 320q^{22} \) \(\mathstrut +\mathstrut 956q^{24} \) \(\mathstrut -\mathstrut 1962q^{25} \) \(\mathstrut +\mathstrut 1008q^{26} \) \(\mathstrut -\mathstrut 1540q^{27} \) \(\mathstrut +\mathstrut 720q^{28} \) \(\mathstrut +\mathstrut 2468q^{30} \) \(\mathstrut +\mathstrut 3924q^{31} \) \(\mathstrut +\mathstrut 3624q^{32} \) \(\mathstrut +\mathstrut 1868q^{33} \) \(\mathstrut +\mathstrut 5036q^{34} \) \(\mathstrut -\mathstrut 5184q^{35} \) \(\mathstrut -\mathstrut 2772q^{36} \) \(\mathstrut -\mathstrut 2808q^{37} \) \(\mathstrut -\mathstrut 6360q^{38} \) \(\mathstrut -\mathstrut 5928q^{39} \) \(\mathstrut -\mathstrut 5416q^{40} \) \(\mathstrut +\mathstrut 720q^{41} \) \(\mathstrut -\mathstrut 8084q^{42} \) \(\mathstrut +\mathstrut 9080q^{43} \) \(\mathstrut -\mathstrut 6720q^{44} \) \(\mathstrut +\mathstrut 2752q^{45} \) \(\mathstrut -\mathstrut 5096q^{46} \) \(\mathstrut +\mathstrut 6264q^{48} \) \(\mathstrut -\mathstrut 4034q^{49} \) \(\mathstrut +\mathstrut 5394q^{50} \) \(\mathstrut -\mathstrut 320q^{51} \) \(\mathstrut +\mathstrut 14080q^{52} \) \(\mathstrut +\mathstrut 14726q^{54} \) \(\mathstrut +\mathstrut 8056q^{55} \) \(\mathstrut +\mathstrut 7512q^{56} \) \(\mathstrut +\mathstrut 1272q^{57} \) \(\mathstrut +\mathstrut 7620q^{58} \) \(\mathstrut +\mathstrut 13056q^{59} \) \(\mathstrut -\mathstrut 9552q^{60} \) \(\mathstrut +\mathstrut 8584q^{61} \) \(\mathstrut -\mathstrut 8724q^{62} \) \(\mathstrut +\mathstrut 724q^{63} \) \(\mathstrut -\mathstrut 39568q^{64} \) \(\mathstrut -\mathstrut 1344q^{65} \) \(\mathstrut -\mathstrut 37800q^{66} \) \(\mathstrut -\mathstrut 21768q^{67} \) \(\mathstrut -\mathstrut 5616q^{68} \) \(\mathstrut -\mathstrut 7360q^{69} \) \(\mathstrut -\mathstrut 9272q^{70} \) \(\mathstrut +\mathstrut 24980q^{72} \) \(\mathstrut -\mathstrut 15052q^{73} \) \(\mathstrut +\mathstrut 17400q^{74} \) \(\mathstrut +\mathstrut 25852q^{75} \) \(\mathstrut +\mathstrut 50712q^{76} \) \(\mathstrut +\mathstrut 55280q^{78} \) \(\mathstrut -\mathstrut 12588q^{79} \) \(\mathstrut +\mathstrut 28512q^{80} \) \(\mathstrut -\mathstrut 4326q^{81} \) \(\mathstrut +\mathstrut 36180q^{82} \) \(\mathstrut -\mathstrut 24000q^{83} \) \(\mathstrut -\mathstrut 26024q^{84} \) \(\mathstrut +\mathstrut 2816q^{85} \) \(\mathstrut -\mathstrut 34344q^{86} \) \(\mathstrut -\mathstrut 16068q^{87} \) \(\mathstrut -\mathstrut 72560q^{88} \) \(\mathstrut +\mathstrut 15600q^{89} \) \(\mathstrut -\mathstrut 71572q^{90} \) \(\mathstrut -\mathstrut 30096q^{91} \) \(\mathstrut -\mathstrut 48096q^{92} \) \(\mathstrut -\mathstrut 17528q^{93} \) \(\mathstrut -\mathstrut 45864q^{94} \) \(\mathstrut +\mathstrut 44312q^{96} \) \(\mathstrut +\mathstrut 23540q^{97} \) \(\mathstrut +\mathstrut 47778q^{98} \) \(\mathstrut +\mathstrut 41728q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)

We only show spaces with odd 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
24.5.b \(\chi_{24}(19, \cdot)\) 24.5.b.a 8 1
24.5.e \(\chi_{24}(17, \cdot)\) 24.5.e.a 4 1
24.5.g \(\chi_{24}(7, \cdot)\) None 0 1
24.5.h \(\chi_{24}(5, \cdot)\) 24.5.h.a 1 1
24.5.h.b 1
24.5.h.c 12

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)