Properties

Label 48.22
Level 48
Weight 22
Dimension 563
Nonzero newspaces 4
Sturm bound 2816
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(2816\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(48))\).

Total New Old
Modular forms 1372 571 801
Cusp forms 1316 563 753
Eisenstein series 56 8 48

Trace form

\( 563 q + 59047 q^{3} - 3208664 q^{4} + 20783558 q^{5} + 142760908 q^{6} + 3921368 q^{7} + 10875501588 q^{8} + 58634199111 q^{9} + O(q^{10}) \) \( 563 q + 59047 q^{3} - 3208664 q^{4} + 20783558 q^{5} + 142760908 q^{6} + 3921368 q^{7} + 10875501588 q^{8} + 58634199111 q^{9} + 203794241504 q^{10} - 201999962220 q^{11} - 366511438088 q^{12} - 425042668434 q^{13} - 7580676743484 q^{14} - 5766503906250 q^{15} - 19346727773104 q^{16} + 1740714497002 q^{17} + 38736889598032 q^{18} + 174854315043152 q^{19} + 196422031250000 q^{20} - 18994655030156 q^{21} + 150959445555000 q^{22} - 418452746476856 q^{23} - 543163857277332 q^{24} - 2225726856549715 q^{25} - 753312645084980 q^{26} - 941848663755869 q^{27} + 5971516838613120 q^{28} + 188716292275198 q^{29} - 9861346794423140 q^{30} + 17030894945943024 q^{31} - 10070930361655680 q^{32} - 14021349681046936 q^{33} + 101761981846555272 q^{34} - 24420616782470376 q^{35} - 121573282713801328 q^{36} + 132588504477350550 q^{37} + 175187804522404712 q^{38} - 167655571739984878 q^{39} - 143311877037888824 q^{40} + 150420339888752034 q^{41} - 191070335613005844 q^{42} + 110501765390601504 q^{43} - 182643993443571464 q^{44} - 571146378416567622 q^{45} + 405098148452892032 q^{46} - 17462175811351488 q^{47} + 609215008489840416 q^{48} + 10543077933473296447 q^{49} - 1465068799295972508 q^{50} + 2623474691920519794 q^{51} + 5852564414089701872 q^{52} - 3759614744263166762 q^{53} + 2330634420068591924 q^{54} + 9648039180388601120 q^{55} - 8134614321801781632 q^{56} + 10316398651018154520 q^{57} + 9907066428017003848 q^{58} + 9676438888472473916 q^{59} - 26888744297706805864 q^{60} - 33781039210679996562 q^{61} + 37423926077749156092 q^{62} + 7893115327721582568 q^{63} - 34141024632214304192 q^{64} + 400598053845283716 q^{65} + 95956051941715322572 q^{66} + 18234570068388076592 q^{67} - 88677994614761171936 q^{68} - 30549477184661057636 q^{69} + 8411622145275193368 q^{70} + 29401064349889550264 q^{71} - 69709252294426783388 q^{72} - 137353912505976851114 q^{73} + 52823343512087181932 q^{74} - 48191100582519692491 q^{75} + 223946943242677147696 q^{76} + 179123046061605469136 q^{77} - 144661561155495490536 q^{78} - 590357105167388337584 q^{79} + 598479047524721480968 q^{80} - 1226123357243779154749 q^{81} - 788564574863045609960 q^{82} - 482217133235447500164 q^{83} + 298974331234753553944 q^{84} + 1245504822526267239644 q^{85} - 1133736219623245285424 q^{86} + 1181232655219292337258 q^{87} - 1999298059630610956480 q^{88} + 298080922501213062882 q^{89} + 1890608458027612425272 q^{90} + 318106672552773102976 q^{91} - 4114711634977220502992 q^{92} - 1458147516457987648544 q^{93} + 1081718229679723851464 q^{94} - 672420598507790817976 q^{95} - 674646009390532316792 q^{96} - 1594002130772077371050 q^{97} - 9484196106654323201240 q^{98} + 394416705631392065888 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.22.a \(\chi_{48}(1, \cdot)\) 48.22.a.a 1 1
48.22.a.b 1
48.22.a.c 1
48.22.a.d 1
48.22.a.e 1
48.22.a.f 1
48.22.a.g 2
48.22.a.h 2
48.22.a.i 2
48.22.a.j 3
48.22.a.k 3
48.22.a.l 3
48.22.c \(\chi_{48}(47, \cdot)\) 48.22.c.a 2 1
48.22.c.b 12
48.22.c.c 28
48.22.d \(\chi_{48}(25, \cdot)\) None 0 1
48.22.f \(\chi_{48}(23, \cdot)\) None 0 1
48.22.j \(\chi_{48}(13, \cdot)\) n/a 168 2
48.22.k \(\chi_{48}(11, \cdot)\) n/a 332 2

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

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)