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Properties

Label 192.8
Level 192
Weight 8
Dimension 3002
Nonzero newspaces 8
Sturm bound 16384
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(16384\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(192))\).

Total New Old
Modular forms 7312 3046 4266
Cusp forms 7024 3002 4022
Eisenstein series 288 44 244

Trace form

\( 3002 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} + O(q^{10}) \) \( 3002 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} + 2408 q^{11} - 8 q^{12} + 14112 q^{13} - 27008 q^{15} - 16 q^{16} + 11632 q^{17} - 8 q^{18} + 121156 q^{19} - 36188 q^{21} - 548928 q^{22} + 598032 q^{24} + 27238 q^{25} - 1455920 q^{26} - 238050 q^{27} - 781856 q^{28} + 206752 q^{29} + 1739912 q^{30} + 714952 q^{31} + 2142640 q^{32} + 391684 q^{33} - 806336 q^{34} - 816504 q^{35} - 4069528 q^{36} - 1662320 q^{37} - 2489840 q^{38} + 283940 q^{39} + 5372704 q^{40} + 3530272 q^{41} + 3858912 q^{42} - 366196 q^{43} - 6740944 q^{44} + 792956 q^{45} - 16 q^{46} - 8 q^{48} - 1647114 q^{49} + 4634832 q^{50} + 6361720 q^{51} - 20409904 q^{52} + 314920 q^{54} - 20955048 q^{55} + 21474544 q^{56} - 1725140 q^{57} + 20716256 q^{58} - 9179680 q^{59} - 4336424 q^{60} - 16 q^{61} - 20695008 q^{62} + 10001880 q^{63} - 45674320 q^{64} + 1520528 q^{65} - 7515240 q^{66} - 18891644 q^{67} + 17500128 q^{68} + 1882924 q^{69} + 71980592 q^{70} - 49394816 q^{71} - 8 q^{72} + 5672940 q^{73} - 8428784 q^{74} + 29037338 q^{75} - 77885840 q^{76} - 15375984 q^{77} + 9862288 q^{78} - 18412216 q^{79} + 63108912 q^{80} - 39201358 q^{81} - 16 q^{82} - 503480 q^{83} + 17056808 q^{84} + 21231872 q^{85} + 40789108 q^{87} - 16 q^{88} + 19124192 q^{89} + 31733992 q^{90} + 1768304 q^{91} - 42564464 q^{93} - 16 q^{94} - 64673232 q^{95} - 112868992 q^{96} - 22760636 q^{97} + 6456500 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.8.a \(\chi_{192}(1, \cdot)\) 192.8.a.a 1 1
192.8.a.b 1
192.8.a.c 1
192.8.a.d 1
192.8.a.e 1
192.8.a.f 1
192.8.a.g 1
192.8.a.h 1
192.8.a.i 1
192.8.a.j 1
192.8.a.k 1
192.8.a.l 1
192.8.a.m 1
192.8.a.n 1
192.8.a.o 1
192.8.a.p 1
192.8.a.q 2
192.8.a.r 2
192.8.a.s 2
192.8.a.t 2
192.8.a.u 2
192.8.a.v 2
192.8.c \(\chi_{192}(191, \cdot)\) 192.8.c.a 2 1
192.8.c.b 4
192.8.c.c 4
192.8.c.d 8
192.8.c.e 8
192.8.c.f 28
192.8.d \(\chi_{192}(97, \cdot)\) 192.8.d.a 4 1
192.8.d.b 4
192.8.d.c 8
192.8.d.d 12
192.8.f \(\chi_{192}(95, \cdot)\) 192.8.f.a 4 1
192.8.f.b 4
192.8.f.c 16
192.8.f.d 32
192.8.j \(\chi_{192}(49, \cdot)\) 192.8.j.a 56 2
192.8.k \(\chi_{192}(47, \cdot)\) n/a 108 2
192.8.n \(\chi_{192}(25, \cdot)\) None 0 4
192.8.o \(\chi_{192}(23, \cdot)\) None 0 4
192.8.r \(\chi_{192}(13, \cdot)\) n/a 896 8
192.8.s \(\chi_{192}(11, \cdot)\) n/a 1776 8

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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