Properties

Label 48.26
Level 48
Weight 26
Dimension 671
Nonzero newspaces 4
Sturm bound 3328
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(3328\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(48))\).

Total New Old
Modular forms 1628 679 949
Cusp forms 1572 671 901
Eisenstein series 56 8 48

Trace form

\( 671 q + 531439 q^{3} + 71440552 q^{4} - 306268562 q^{5} - 5523305588 q^{6} - 63411416648 q^{7} + 223171593108 q^{8} + 8136916311459 q^{9} + O(q^{10}) \) \( 671 q + 531439 q^{3} + 71440552 q^{4} - 306268562 q^{5} - 5523305588 q^{6} - 63411416648 q^{7} + 223171593108 q^{8} + 8136916311459 q^{9} - 22408938559136 q^{10} + 42002332228788 q^{11} - 4457958449480 q^{12} - 142495589948410 q^{13} - 1139571992122044 q^{14} - 1297463378906250 q^{15} - 5673802170667184 q^{16} + 1186009327105202 q^{17} - 18877596795723632 q^{18} - 34322308835547856 q^{19} - 50483667968750000 q^{20} + 64078134682053412 q^{21} - 45314558139907784 q^{22} - 210628999613059192 q^{23} - 475668915229785492 q^{24} - 1474711887351062655 q^{25} + 2124873935607267020 q^{26} - 1604801042290117349 q^{27} + 2997740175355336320 q^{28} + 290777331959938790 q^{29} - 10347470579349912740 q^{30} + 10849148448203058640 q^{31} + 2739094884515808000 q^{32} + 6401265890100823832 q^{33} + 41260426890124502152 q^{34} + 22865276432669932824 q^{35} + 8143017466365710480 q^{36} + 62893538368440977006 q^{37} - 67280104521783674648 q^{38} + 49631253377802884498 q^{39} + 547917411476528901576 q^{40} + 63829338646905784362 q^{41} + 522141044792625220716 q^{42} - 197254793409605643840 q^{43} - 618755518097427318664 q^{44} - 70821741615300104862 q^{45} - 3657116543983692516096 q^{46} + 2339689137142659822720 q^{47} - 3013264732397007328224 q^{48} + 24416716085771087900091 q^{49} + 9459843554895724915812 q^{50} + 8532259221167245681410 q^{51} - 6912053143682661160592 q^{52} + 17726063573794732302974 q^{53} - 15169376444165606460364 q^{54} - 224608499625661212640 q^{55} + 30451490612476869503232 q^{56} + 28002593330262408009912 q^{57} - 6566183024011877098424 q^{58} + 38886063728638924834012 q^{59} + 15769330554893395922456 q^{60} - 100194326661148982313786 q^{61} - 65785670349702341510532 q^{62} + 13364249618591852593608 q^{63} + 260112848418357580558144 q^{64} + 74112242176077446865876 q^{65} - 250721407988534025357428 q^{66} + 462274685190180606686416 q^{67} + 583082846239535086631072 q^{68} - 674382076704784562103524 q^{69} + 290176981134652956739608 q^{70} - 305471954924433131163272 q^{71} - 187340456394177222770204 q^{72} - 1305307806958144730515410 q^{73} + 1326896444783693960665324 q^{74} - 259047671329404949535971 q^{75} - 398656711360042232271440 q^{76} - 429161818569642196640624 q^{77} - 1229510387678932137855912 q^{78} - 3078018198182256242508112 q^{79} + 5778907049821275717759368 q^{80} - 15065670705533271265369009 q^{81} - 8314574408971963301838696 q^{82} - 4548518187556328211551076 q^{83} + 12175626121261418503113880 q^{84} + 511313080135047324458604 q^{85} - 1675845412653628081467952 q^{86} - 1557962876209661305819254 q^{87} + 4240410808433170143969088 q^{88} + 3618649100407410002267562 q^{89} - 26951628466862836807186888 q^{90} + 7364539789002981332183360 q^{91} + 12306996435575049591700784 q^{92} - 15012347260112029612710896 q^{93} - 12413057613746700251574328 q^{94} - 16901937290686977585112376 q^{95} - 4666227284976050842781816 q^{96} - 34120648854336971491459474 q^{97} + 36174793225968696715471400 q^{98} + 572479458250749699225728 q^{99} + O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(48))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
48.26.a \(\chi_{48}(1, \cdot)\) 48.26.a.a 1 1
48.26.a.b 1
48.26.a.c 1
48.26.a.d 2
48.26.a.e 2
48.26.a.f 2
48.26.a.g 3
48.26.a.h 3
48.26.a.i 3
48.26.a.j 3
48.26.a.k 4
48.26.c \(\chi_{48}(47, \cdot)\) 48.26.c.a 2 1
48.26.c.b 16
48.26.c.c 32
48.26.d \(\chi_{48}(25, \cdot)\) None 0 1
48.26.f \(\chi_{48}(23, \cdot)\) None 0 1
48.26.j \(\chi_{48}(13, \cdot)\) n/a 200 2
48.26.k \(\chi_{48}(11, \cdot)\) n/a 396 2

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

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)