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Properties

Label 24.11
Level 24
Weight 11
Dimension 68
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 352
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(352\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(24))\).

Total New Old
Modular forms 172 72 100
Cusp forms 148 68 80
Eisenstein series 24 4 20

Trace form

\( 68 q - 22 q^{2} - 22 q^{3} - 2476 q^{4} - 12062 q^{6} - 5440 q^{7} + 118076 q^{8} + 364724 q^{9} + O(q^{10}) \) \( 68 q - 22 q^{2} - 22 q^{3} - 2476 q^{4} - 12062 q^{6} - 5440 q^{7} + 118076 q^{8} + 364724 q^{9} - 274412 q^{10} - 91808 q^{11} + 1033936 q^{12} - 124508 q^{13} - 503244 q^{14} - 745908 q^{15} + 1048608 q^{16} - 905768 q^{17} + 1877078 q^{18} - 10000524 q^{19} - 5944248 q^{20} - 3929724 q^{21} + 2281984 q^{22} - 18426868 q^{24} + 312048 q^{25} + 19400160 q^{26} - 3536326 q^{27} - 49449072 q^{28} - 36072412 q^{30} + 54116832 q^{31} + 118772648 q^{32} + 24147572 q^{33} + 141028460 q^{34} - 68411424 q^{35} - 132124212 q^{36} + 89985156 q^{37} - 119065400 q^{38} + 192608148 q^{39} + 195377528 q^{40} + 51872200 q^{41} - 5055140 q^{42} - 232698604 q^{43} - 333411776 q^{44} + 39125824 q^{45} - 1506874760 q^{46} + 558031032 q^{48} + 543602596 q^{49} + 2330181842 q^{50} + 760586656 q^{51} - 3357381920 q^{52} - 846895498 q^{54} - 177851816 q^{55} + 4216587096 q^{56} - 59583300 q^{57} + 1375687908 q^{58} - 1499085440 q^{59} + 726795888 q^{60} - 101460764 q^{61} - 5504139012 q^{62} + 2606796832 q^{63} + 4055240432 q^{64} + 1717119456 q^{65} + 2793739896 q^{66} - 7584620844 q^{67} - 6509360144 q^{68} - 3501669184 q^{69} - 8435987480 q^{70} + 4507268036 q^{72} + 2532339752 q^{73} + 7298736360 q^{74} + 11314049818 q^{75} - 7262701128 q^{76} + 582088160 q^{78} - 26249507232 q^{79} + 4230593184 q^{80} - 1538549340 q^{81} + 6831890292 q^{82} + 14192131360 q^{83} - 339238184 q^{84} + 18713636096 q^{85} + 11933558200 q^{86} - 5769792084 q^{87} - 3909180464 q^{88} + 8963359000 q^{89} - 3994700116 q^{90} - 18315040824 q^{91} + 13243366752 q^{92} - 24272938652 q^{93} - 265321800 q^{94} - 3898628392 q^{96} + 65075235656 q^{97} - 20615960782 q^{98} + 41701440352 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(24))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
24.11.b \(\chi_{24}(19, \cdot)\) 24.11.b.a 20 1
24.11.e \(\chi_{24}(17, \cdot)\) 24.11.e.a 10 1
24.11.g \(\chi_{24}(7, \cdot)\) None 0 1
24.11.h \(\chi_{24}(5, \cdot)\) 24.11.h.a 1 1
24.11.h.b 1
24.11.h.c 36

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)