Properties

Label 48.28
Level 48
Weight 28
Dimension 725
Nonzero newspaces 4
Sturm bound 3584
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 28 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(3584\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_1(48))\).

Total New Old
Modular forms 1756 733 1023
Cusp forms 1700 725 975
Eisenstein series 56 8 48

Trace form

\( 725 q - 1594325 q^{3} - 250191384 q^{4} + 2726446322 q^{5} + 59499919468 q^{6} + 314746286424 q^{7} + 574361867604 q^{8} + 52953654534753 q^{9} + O(q^{10}) \) \( 725 q - 1594325 q^{3} - 250191384 q^{4} + 2726446322 q^{5} + 59499919468 q^{6} + 314746286424 q^{7} + 574361867604 q^{8} + 52953654534753 q^{9} - 16494420470752 q^{10} + 102119465430660 q^{11} - 1748989708884584 q^{12} + 514238999348866 q^{13} + 14310437170500228 q^{14} + 19461950683593750 q^{15} + 88133012225241296 q^{16} - 19308849445239146 q^{17} + 151690932494393776 q^{18} + 439353629161008992 q^{19} + 1506192207031250000 q^{20} - 1788491555723047652 q^{21} + 8938908434340382264 q^{22} - 3605769732956008568 q^{23} + 15187189433744993388 q^{24} - 48650958049504425701 q^{25} - 16920893255094036020 q^{26} + 12915719179301923759 q^{27} - 12773240204473083520 q^{28} + 68593554719160631978 q^{29} + 101716319036066431420 q^{30} - 525389262159692812176 q^{31} + 1169600394941455275840 q^{32} + 489854725710400055120 q^{33} + 1129458329114403078536 q^{34} + 796071030676812495480 q^{35} + 1006679057039606628368 q^{36} - 2175699024290925023126 q^{37} + 1297404346755636263336 q^{38} - 9751559583591440159038 q^{39} + 1143403892696725672776 q^{40} - 5197757424407616932658 q^{41} + 30449578126572456403116 q^{42} - 35868306213039817112240 q^{43} - 52461449140051092163016 q^{44} - 11704232481120454618746 q^{45} + 7279262486311074043584 q^{46} - 26204361341315254001856 q^{47} + 50687574638143157399712 q^{48} + 1448904742988288198575961 q^{49} - 530329619151843324195612 q^{50} - 130147899131204361562086 q^{51} + 1054737552355865928876848 q^{52} - 336815522402830263373886 q^{53} + 226780220828013233958836 q^{54} + 413554274942248175824608 q^{55} - 1763984545166965006302144 q^{56} - 2758064634546957613294680 q^{57} + 5918266256418873594518472 q^{58} - 280330630402616113081012 q^{59} - 2661949550650125963525544 q^{60} + 857869586501931079456354 q^{61} + 8665698329608506792900924 q^{62} - 1170188087478376877427096 q^{63} - 20814341173622986231228992 q^{64} + 1956406612740303457974588 q^{65} - 3219617529492694820718356 q^{66} - 55678251119529586186087552 q^{67} + 8855668157442147356761312 q^{68} + 32564638115570119023961756 q^{69} + 14337673068876742134923288 q^{70} - 9874520673380575154228872 q^{71} - 31919991301952486746783196 q^{72} + 110605130270579082130977338 q^{73} - 87906462349433607289606612 q^{74} + 58134998748516361258058681 q^{75} + 211525966995617504558859888 q^{76} - 156224527581924285752739088 q^{77} - 61743674844624433535281800 q^{78} + 108373074712172564601453008 q^{79} + 113202077632773448639507912 q^{80} - 1144999628776539613740549451 q^{81} + 44271657724039709147532248 q^{82} + 581453039702265756373235628 q^{83} + 56614067264598441641793496 q^{84} - 113285363032065553378099308 q^{85} + 864024318743526433798324432 q^{86} + 678977150836040610397401210 q^{87} - 148905226392035567538918592 q^{88} - 179257875026818440382974354 q^{89} + 1158616555879871162000166200 q^{90} + 1282675767266279619265674304 q^{91} - 1017412224654144957499163984 q^{92} - 597698048296730009461800632 q^{93} + 716790530933013503868411976 q^{94} + 3009672643351660951302190664 q^{95} + 1518112391937862772808863368 q^{96} - 258666249284081907112656902 q^{97} - 922979840679433969910083160 q^{98} + 2101524041421186058384084304 q^{99} + O(q^{100}) \)

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.28.a \(\chi_{48}(1, \cdot)\) 48.28.a.a 1 1
48.28.a.b 1
48.28.a.c 1
48.28.a.d 2
48.28.a.e 2
48.28.a.f 2
48.28.a.g 2
48.28.a.h 3
48.28.a.i 3
48.28.a.j 3
48.28.a.k 3
48.28.a.l 4
48.28.c \(\chi_{48}(47, \cdot)\) 48.28.c.a 2 1
48.28.c.b 16
48.28.c.c 36
48.28.d \(\chi_{48}(25, \cdot)\) None 0 1
48.28.f \(\chi_{48}(23, \cdot)\) None 0 1
48.28.j \(\chi_{48}(13, \cdot)\) n/a 216 2
48.28.k \(\chi_{48}(11, \cdot)\) n/a 428 2

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

Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{28}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{28}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 1}\)