Properties

Label 75.22
Level 75
Weight 22
Dimension 2882
Nonzero newspaces 6
Sturm bound 8800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(8800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(75))\).

Total New Old
Modular forms 4256 2922 1334
Cusp forms 4144 2882 1262
Eisenstein series 112 40 72

Trace form

\( 2882 q + 3646 q^{2} - 244510 q^{3} - 4523680 q^{4} + 12461214 q^{5} + 365451972 q^{6} + 225120804 q^{7} + 23900356944 q^{8} - 10 q^{9} + O(q^{10}) \) \( 2882 q + 3646 q^{2} - 244510 q^{3} - 4523680 q^{4} + 12461214 q^{5} + 365451972 q^{6} + 225120804 q^{7} + 23900356944 q^{8} - 10 q^{9} + 130191716736 q^{10} - 260117150000 q^{11} + 1745880921554 q^{12} - 2655216866884 q^{13} + 16767597108000 q^{14} - 8819596425304 q^{15} + 139457041324236 q^{16} - 40856171969320 q^{17} + 15396955063796 q^{18} - 26394935728580 q^{19} - 464975687591844 q^{20} - 13173821441178 q^{21} - 1132233135388220 q^{22} + 229832026270832 q^{23} + 3203075537228520 q^{24} - 3270313474292086 q^{25} - 528518872750620 q^{26} - 4498666261587910 q^{27} - 4701012068140132 q^{28} - 31228866573811280 q^{29} + 14391445428588434 q^{30} + 10090199762778764 q^{31} - 55675054472070536 q^{32} + 42991785723081278 q^{33} - 35440469758493560 q^{34} + 85909851743065280 q^{35} - 169165763595309406 q^{36} + 281400070406195894 q^{37} - 327862673901670532 q^{38} + 171616207324863870 q^{39} - 345674277491243688 q^{40} + 408759850984674520 q^{41} - 51662170787400318 q^{42} - 1615244863541322476 q^{43} - 1549933058699454180 q^{44} + 2413511938029434644 q^{45} - 3987310327688434236 q^{46} - 5214667116712347232 q^{47} + 8414741317181455936 q^{48} + 5605627924496238570 q^{49} - 3683958849391043644 q^{50} + 3276428672619620072 q^{51} + 10590288538410438920 q^{52} + 7053598922788952722 q^{53} + 14263897566001078530 q^{54} - 19209045411887238476 q^{55} + 16232237899700799480 q^{56} - 8981430909933381362 q^{57} + 40990033746781037476 q^{58} - 23982542829690790480 q^{59} - 65059367664950635606 q^{60} + 14940748124066029364 q^{61} + 74633710830178174268 q^{62} + 17904975280163284954 q^{63} - 81000135564294359080 q^{64} + 80590237837574582122 q^{65} - 45616949031368769930 q^{66} + 54660948776712504180 q^{67} + 186362918048685996632 q^{68} - 250350822163960675730 q^{69} - 125311074082420002140 q^{70} + 217732029177619324160 q^{71} + 918044026447493660694 q^{72} + 107575971741786762812 q^{73} - 1117372235423410838140 q^{74} - 18879963280837739964 q^{75} + 1605858821193287254968 q^{76} + 1109136767056664580288 q^{77} - 1023297315606706757240 q^{78} - 894595603391694070180 q^{79} - 598419851130970219724 q^{80} - 1028225685712722412498 q^{81} + 3796567433216497553928 q^{82} - 2374973938812454723712 q^{83} - 3125774390426634369370 q^{84} + 2485786583064202069278 q^{85} + 292233290512249960240 q^{86} + 2512246730205445501146 q^{87} + 5095039569480693603244 q^{88} - 539141442705503879490 q^{89} + 221707441097139185006 q^{90} - 1589017667276382302996 q^{91} + 10375149755934484542664 q^{92} + 6804484840228118993926 q^{93} - 2070805455344968185700 q^{94} - 3180439489448637998024 q^{95} + 6348534596532116870226 q^{96} - 6467501450401058091260 q^{97} + 2632091937977758502614 q^{98} - 740270045738270767680 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(75))\)

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
75.22.a \(\chi_{75}(1, \cdot)\) 75.22.a.a 1 1
75.22.a.b 1
75.22.a.c 1
75.22.a.d 2
75.22.a.e 3
75.22.a.f 3
75.22.a.g 3
75.22.a.h 4
75.22.a.i 6
75.22.a.j 6
75.22.a.k 8
75.22.a.l 8
75.22.a.m 10
75.22.a.n 10
75.22.b \(\chi_{75}(49, \cdot)\) 75.22.b.a 2 1
75.22.b.b 2
75.22.b.c 2
75.22.b.d 4
75.22.b.e 6
75.22.b.f 6
75.22.b.g 6
75.22.b.h 8
75.22.b.i 12
75.22.b.j 16
75.22.e \(\chi_{75}(32, \cdot)\) n/a 248 2
75.22.g \(\chi_{75}(16, \cdot)\) n/a 424 4
75.22.i \(\chi_{75}(4, \cdot)\) n/a 416 4
75.22.l \(\chi_{75}(2, \cdot)\) n/a 1664 8

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

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)