Properties

Label 192.12
Level 192
Weight 12
Dimension 4730
Nonzero newspaces 8
Sturm bound 24576
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(24576\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(192))\).

Total New Old
Modular forms 11408 4774 6634
Cusp forms 11120 4730 6390
Eisenstein series 288 44 244

Trace form

\( 4730 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} + O(q^{10}) \) \( 4730 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} - 1081688 q^{11} - 8 q^{12} + 6175456 q^{13} - 6075008 q^{15} - 16 q^{16} + 21117872 q^{17} - 8 q^{18} - 22582588 q^{19} - 838844 q^{21} + 1023936 q^{22} - 356568048 q^{24} + 371113798 q^{25} + 870480080 q^{26} - 66817602 q^{27} - 1435436576 q^{28} - 310692832 q^{29} + 1045605512 q^{30} + 687099592 q^{31} + 1515542960 q^{32} - 441046364 q^{33} - 3615260096 q^{34} - 1064775864 q^{35} + 80564072 q^{36} + 2091048208 q^{37} + 7210484240 q^{38} + 579959972 q^{39} - 8790531296 q^{40} - 5389929568 q^{41} + 1501551072 q^{42} + 2884696652 q^{43} - 10630206416 q^{44} - 531444964 q^{45} - 16 q^{46} - 8 q^{48} - 3954653514 q^{49} - 36807724848 q^{50} - 7748282120 q^{51} + 56046072272 q^{52} - 5280397784 q^{54} + 95614027352 q^{55} - 41745629968 q^{56} - 3650305652 q^{57} + 85948359392 q^{58} - 114963902240 q^{59} + 41245373656 q^{60} - 16 q^{61} - 67461330912 q^{62} + 39697461720 q^{63} - 159579746128 q^{64} - 12733372592 q^{65} + 55611066264 q^{66} - 209200598524 q^{67} + 142040213472 q^{68} - 32003287796 q^{69} - 12530223568 q^{70} + 174711608192 q^{71} - 8 q^{72} + 116941473772 q^{73} - 71681877232 q^{74} - 83741124742 q^{75} + 480084692592 q^{76} - 40454966064 q^{77} - 12986835824 q^{78} + 424682552904 q^{79} - 168509389008 q^{80} + 126933780146 q^{81} - 16 q^{82} + 122796947720 q^{83} - 409345172440 q^{84} + 197214869312 q^{85} - 50128110092 q^{87} - 16 q^{88} - 208699134368 q^{89} + 862428149992 q^{90} - 85325935888 q^{91} - 46523351600 q^{93} - 16 q^{94} + 256184809008 q^{95} - 939816536704 q^{96} - 44752872444 q^{97} + 188241133748 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(192))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
192.12.a \(\chi_{192}(1, \cdot)\) 192.12.a.a 1 1
192.12.a.b 1
192.12.a.c 1
192.12.a.d 1
192.12.a.e 1
192.12.a.f 1
192.12.a.g 1
192.12.a.h 1
192.12.a.i 1
192.12.a.j 1
192.12.a.k 1
192.12.a.l 1
192.12.a.m 1
192.12.a.n 1
192.12.a.o 1
192.12.a.p 1
192.12.a.q 1
192.12.a.r 1
192.12.a.s 1
192.12.a.t 1
192.12.a.u 2
192.12.a.v 2
192.12.a.w 2
192.12.a.x 2
192.12.a.y 2
192.12.a.z 2
192.12.a.ba 3
192.12.a.bb 3
192.12.a.bc 3
192.12.a.bd 3
192.12.c \(\chi_{192}(191, \cdot)\) 192.12.c.a 2 1
192.12.c.b 8
192.12.c.c 12
192.12.c.d 20
192.12.c.e 44
192.12.d \(\chi_{192}(97, \cdot)\) 192.12.d.a 8 1
192.12.d.b 8
192.12.d.c 12
192.12.d.d 16
192.12.f \(\chi_{192}(95, \cdot)\) 192.12.f.a 4 1
192.12.f.b 4
192.12.f.c 24
192.12.f.d 56
192.12.j \(\chi_{192}(49, \cdot)\) 192.12.j.a 88 2
192.12.k \(\chi_{192}(47, \cdot)\) n/a 172 2
192.12.n \(\chi_{192}(25, \cdot)\) None 0 4
192.12.o \(\chi_{192}(23, \cdot)\) None 0 4
192.12.r \(\chi_{192}(13, \cdot)\) n/a 1408 8
192.12.s \(\chi_{192}(11, \cdot)\) n/a 2800 8

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(192)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)