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Properties

Label 48.24
Level 48
Weight 24
Dimension 617
Nonzero newspaces 4
Sturm bound 3072
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 24 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(3072\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(48))\).

Total New Old
Modular forms 1500 625 875
Cusp forms 1444 617 827
Eisenstein series 56 8 48

Trace form

\( 617 q - 177149 q^{3} + 20101992 q^{4} - 35553398 q^{5} + 34901164 q^{6} + 27593272 q^{7} - 61280246316 q^{8} + 729298102341 q^{9} + O(q^{10}) \) \( 617 q - 177149 q^{3} + 20101992 q^{4} - 35553398 q^{5} + 34901164 q^{6} + 27593272 q^{7} - 61280246316 q^{8} + 729298102341 q^{9} + 1177114946208 q^{10} - 2926722800028 q^{11} + 10365979822552 q^{12} + 2055170471978 q^{13} + 24161501993988 q^{14} + 86497558593750 q^{15} + 342792402599376 q^{16} - 56302527224626 q^{17} + 398611994387824 q^{18} - 767380396944256 q^{19} - 1872342968750000 q^{20} - 1466304402739220 q^{21} - 9764640575390664 q^{22} + 5921082022875464 q^{23} - 161525454858132 q^{24} - 49587888926220921 q^{25} - 59838318056660020 q^{26} + 62640886506132439 q^{27} - 164062437749353600 q^{28} - 81143270691395710 q^{29} + 249540376199608060 q^{30} - 293011500350433712 q^{31} - 532722654506952000 q^{32} - 367928489725492576 q^{33} - 3178773424093190264 q^{34} + 410340072577756920 q^{35} + 3141273557426746640 q^{36} - 1242247266631774894 q^{37} - 3392793966871378904 q^{38} + 11214230311184138498 q^{39} - 13717992707892125624 q^{40} - 3652830720208460346 q^{41} - 3934571727390860244 q^{42} + 344220446721811888 q^{43} - 85145389869359997256 q^{44} + 40895863741677366174 q^{45} + 43424137374114043712 q^{46} - 33778365706201587840 q^{47} + 3728632774265699232 q^{48} + 602358471399752378205 q^{49} - 59010837258340312092 q^{50} - 133201902060213092022 q^{51} + 117011355166638033840 q^{52} - 123679209481377576358 q^{53} + 167355987369316441268 q^{54} - 132900130796444604192 q^{55} - 90379237811130289728 q^{56} - 125851061055148200696 q^{57} - 237697368749747508024 q^{58} - 910842782171597343956 q^{59} - 853031075062850840104 q^{60} + 2213955940538975523658 q^{61} - 953585531691197894724 q^{62} - 495538960743934760376 q^{63} + 4533031890054479265984 q^{64} - 1561603706581937911572 q^{65} + 774220244498467159084 q^{66} - 288828515346981423264 q^{67} - 2082038477856096624544 q^{68} + 2915802095175619111708 q^{69} + 6709351054558158946328 q^{70} - 3056895351026800555976 q^{71} + 7794617485999790436772 q^{72} + 2853302015783455088610 q^{73} + 5481770393543905675180 q^{74} + 2878761143520461592881 q^{75} - 46921442586915791025936 q^{76} + 17476426489669480290352 q^{77} + 32076860739728265400632 q^{78} + 17451091954732861983280 q^{79} - 22277011318884806383288 q^{80} - 183582238447970997489751 q^{81} + 120990589302461553129816 q^{82} + 9438353779231817427852 q^{83} - 152954087095912164339368 q^{84} - 72971500078380208122748 q^{85} + 79497921536638972529360 q^{86} - 51634949225571834486054 q^{87} - 110988123670844865094848 q^{88} - 17769723919775888095194 q^{89} + 130526511434613103713080 q^{90} - 199243357154067012948480 q^{91} + 165179375591045694834608 q^{92} + 303716974104952716312472 q^{93} - 369775087320757016953016 q^{94} - 715297309526594170490936 q^{95} - 233483369412650315556728 q^{96} + 397230237203857506566370 q^{97} + 814587015432048047125160 q^{98} - 126378477389090632977616 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.24.a \(\chi_{48}(1, \cdot)\) 48.24.a.a 1 1
48.24.a.b 1
48.24.a.c 1
48.24.a.d 1
48.24.a.e 2
48.24.a.f 2
48.24.a.g 2
48.24.a.h 2
48.24.a.i 2
48.24.a.j 3
48.24.a.k 3
48.24.a.l 3
48.24.c \(\chi_{48}(47, \cdot)\) 48.24.c.a 2 1
48.24.c.b 16
48.24.c.c 28
48.24.d \(\chi_{48}(25, \cdot)\) None 0 1
48.24.f \(\chi_{48}(23, \cdot)\) None 0 1
48.24.j \(\chi_{48}(13, \cdot)\) n/a 184 2
48.24.k \(\chi_{48}(11, \cdot)\) n/a 364 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)