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Properties

Label 192.10
Level 192
Weight 10
Dimension 3866
Nonzero newspaces 8
Sturm bound 20480
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(20480\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(192))\).

Total New Old
Modular forms 9360 3910 5450
Cusp forms 9072 3866 5206
Eisenstein series 288 44 244

Trace form

\( 3866 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} + O(q^{10}) \) \( 3866 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} + 131720 q^{11} - 8 q^{12} - 389248 q^{13} + 404992 q^{15} - 16 q^{16} - 815984 q^{17} - 8 q^{18} - 961788 q^{19} + 1959220 q^{21} - 7152704 q^{22} - 12097008 q^{24} - 9867882 q^{25} + 4211920 q^{26} + 6325038 q^{27} + 43582944 q^{28} + 2533600 q^{29} - 44263288 q^{30} - 22164536 q^{31} - 58882640 q^{32} + 111892 q^{33} + 77073984 q^{34} + 38240616 q^{35} + 110500712 q^{36} + 4859088 q^{37} - 133894640 q^{38} - 72274204 q^{39} - 194179296 q^{40} + 30247648 q^{41} + 224559072 q^{42} + 38062444 q^{43} - 292354000 q^{44} - 29933812 q^{45} - 16 q^{46} - 8 q^{48} - 80707242 q^{49} - 365516592 q^{50} + 567389368 q^{51} + 50454992 q^{52} + 161558056 q^{54} - 700544168 q^{55} - 406326032 q^{56} - 61143908 q^{57} - 1710306592 q^{58} + 1440376160 q^{59} - 230939432 q^{60} - 16 q^{61} + 1195227168 q^{62} - 630118440 q^{63} + 2729619632 q^{64} - 826427536 q^{65} - 186013800 q^{66} + 2826525252 q^{67} - 2008655904 q^{68} + 607473628 q^{69} - 3738184144 q^{70} + 952405888 q^{71} - 8 q^{72} - 1854238740 q^{73} + 4364366608 q^{74} - 3340229494 q^{75} + 1777421936 q^{76} + 877461168 q^{77} - 1195899248 q^{78} + 7230824904 q^{79} + 1824710448 q^{80} + 384090674 q^{81} - 16 q^{82} - 795523160 q^{83} + 6148771880 q^{84} - 2616531808 q^{85} - 2350951628 q^{87} - 16 q^{88} + 733543712 q^{89} - 7222410008 q^{90} + 2947489584 q^{91} + 3219229360 q^{93} - 16 q^{94} - 4961986512 q^{95} + 10366581632 q^{96} + 679199140 q^{97} + 860643380 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.10.a \(\chi_{192}(1, \cdot)\) 192.10.a.a 1 1
192.10.a.b 1
192.10.a.c 1
192.10.a.d 1
192.10.a.e 1
192.10.a.f 1
192.10.a.g 1
192.10.a.h 1
192.10.a.i 1
192.10.a.j 1
192.10.a.k 1
192.10.a.l 1
192.10.a.m 1
192.10.a.n 1
192.10.a.o 2
192.10.a.p 2
192.10.a.q 2
192.10.a.r 2
192.10.a.s 2
192.10.a.t 2
192.10.a.u 2
192.10.a.v 2
192.10.a.w 3
192.10.a.x 3
192.10.c \(\chi_{192}(191, \cdot)\) 192.10.c.a 2 1
192.10.c.b 4
192.10.c.c 12
192.10.c.d 16
192.10.c.e 36
192.10.d \(\chi_{192}(97, \cdot)\) 192.10.d.a 4 1
192.10.d.b 8
192.10.d.c 12
192.10.d.d 12
192.10.f \(\chi_{192}(95, \cdot)\) 192.10.f.a 4 1
192.10.f.b 4
192.10.f.c 16
192.10.f.d 48
192.10.j \(\chi_{192}(49, \cdot)\) 192.10.j.a 72 2
192.10.k \(\chi_{192}(47, \cdot)\) n/a 140 2
192.10.n \(\chi_{192}(25, \cdot)\) None 0 4
192.10.o \(\chi_{192}(23, \cdot)\) None 0 4
192.10.r \(\chi_{192}(13, \cdot)\) n/a 1152 8
192.10.s \(\chi_{192}(11, \cdot)\) n/a 2288 8

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(192)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)