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Properties

Label 24.12
Level 24
Weight 12
Dimension 69
Nonzero newspaces 3
Newform subspaces 7
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 7 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(24))\).

Total New Old
Modular forms 188 73 115
Cusp forms 164 69 95
Eisenstein series 24 4 20

Trace form

\( 69 q - 46 q^{2} + 241 q^{3} - 876 q^{4} - 2506 q^{5} + 28402 q^{6} + 31636 q^{7} + 187124 q^{8} - 1003835 q^{9} + O(q^{10}) \) \( 69 q - 46 q^{2} + 241 q^{3} - 876 q^{4} - 2506 q^{5} + 28402 q^{6} + 31636 q^{7} + 187124 q^{8} - 1003835 q^{9} + 81956 q^{10} + 658244 q^{11} + 532744 q^{12} - 2322226 q^{13} - 3510532 q^{14} - 759618 q^{15} - 6229600 q^{16} - 11625010 q^{17} + 18804886 q^{18} + 22229536 q^{19} - 46884424 q^{20} - 8135640 q^{21} + 72401376 q^{22} + 32884848 q^{23} + 44947924 q^{24} + 121519031 q^{25} - 111529288 q^{26} + 81166501 q^{27} + 377706672 q^{28} + 318462366 q^{29} - 371159772 q^{30} - 865236060 q^{31} - 430177016 q^{32} + 244682396 q^{33} - 73393876 q^{34} - 170081136 q^{35} + 499659004 q^{36} + 394434486 q^{37} - 750297416 q^{38} + 394063866 q^{39} - 350053496 q^{40} + 99599918 q^{41} - 395088972 q^{42} - 1862654896 q^{43} + 6480991872 q^{44} - 147976794 q^{45} - 6764035672 q^{46} + 4138665144 q^{47} - 3080825864 q^{48} - 5255050175 q^{49} + 11370618050 q^{50} - 5202237466 q^{51} + 11871348560 q^{52} + 1825434182 q^{53} + 1968932446 q^{54} - 14120756488 q^{55} - 22369393480 q^{56} + 3076896368 q^{57} + 25915433556 q^{58} + 1961805716 q^{59} + 8790278448 q^{60} + 4980362462 q^{61} - 39991136540 q^{62} - 6071418180 q^{63} - 73683835920 q^{64} + 25680717460 q^{65} + 38898082760 q^{66} + 50933727784 q^{67} + 70188643872 q^{68} + 1474051608 q^{69} - 94711855432 q^{70} - 61197947312 q^{71} + 21204948412 q^{72} - 70094022862 q^{73} + 72576792800 q^{74} + 88520582815 q^{75} + 107906790088 q^{76} + 21317107680 q^{77} - 85537939944 q^{78} - 128256967740 q^{79} - 125943872832 q^{80} + 83036521861 q^{81} + 191461269028 q^{82} + 103653834748 q^{83} + 82671739320 q^{84} - 136532770292 q^{85} - 212179058872 q^{86} + 99938940966 q^{87} - 31112960784 q^{88} + 98762461622 q^{89} - 102649679316 q^{90} - 43714614480 q^{91} + 305089854912 q^{92} - 82452878208 q^{93} - 262024171992 q^{94} - 62843367688 q^{95} - 83211682280 q^{96} - 156805688758 q^{97} + 103654452522 q^{98} - 87720840076 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(24))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
24.12.a \(\chi_{24}(1, \cdot)\) 24.12.a.a 1 1
24.12.a.b 1
24.12.a.c 1
24.12.a.d 2
24.12.c \(\chi_{24}(23, \cdot)\) None 0 1
24.12.d \(\chi_{24}(13, \cdot)\) 24.12.d.a 22 1
24.12.f \(\chi_{24}(11, \cdot)\) 24.12.f.a 2 1
24.12.f.b 40

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)