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Properties

Label 192.6
Level 192
Weight 6
Dimension 2138
Nonzero newspaces 8
Sturm bound 12288
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(12288\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(192))\).

Total New Old
Modular forms 5264 2182 3082
Cusp forms 4976 2138 2838
Eisenstein series 288 44 244

Trace form

\( 2138 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} + O(q^{10}) \) \( 2138 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} - 1208 q^{11} - 8 q^{12} + 448 q^{13} + 1792 q^{15} - 16 q^{16} + 1616 q^{17} - 8 q^{18} - 4732 q^{19} - 5228 q^{21} - 27200 q^{22} + 22032 q^{24} + 31158 q^{25} + 51920 q^{26} + 3726 q^{27} - 8736 q^{28} - 16288 q^{29} - 64888 q^{30} - 23096 q^{31} - 74320 q^{32} - 23180 q^{33} - 25536 q^{34} + 4776 q^{35} + 62312 q^{36} + 42576 q^{37} + 139280 q^{38} + 44900 q^{39} + 124704 q^{40} + 19808 q^{41} - 46368 q^{42} - 32084 q^{43} - 131024 q^{44} - 48532 q^{45} - 16 q^{46} - 8 q^{48} - 33642 q^{49} + 274128 q^{50} - 60872 q^{51} - 146992 q^{52} - 58328 q^{54} + 550232 q^{55} - 301840 q^{56} + 87868 q^{57} - 52000 q^{58} - 144800 q^{59} + 197848 q^{60} - 16 q^{61} + 351264 q^{62} - 158760 q^{63} + 749744 q^{64} - 40016 q^{65} + 254616 q^{66} - 395068 q^{67} + 14304 q^{68} - 141572 q^{69} - 573904 q^{70} + 575360 q^{71} - 8 q^{72} + 169964 q^{73} - 755440 q^{74} + 552746 q^{75} - 536976 q^{76} + 241008 q^{77} + 722320 q^{78} - 638776 q^{79} + 986928 q^{80} + 94514 q^{81} - 16 q^{82} + 126440 q^{83} - 985048 q^{84} - 31648 q^{85} - 282188 q^{87} - 16 q^{88} - 280928 q^{89} + 284392 q^{90} - 262224 q^{91} + 363376 q^{93} - 16 q^{94} + 76848 q^{95} + 1214336 q^{96} + 26852 q^{97} + 190004 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.6.a \(\chi_{192}(1, \cdot)\) 192.6.a.a 1 1
192.6.a.b 1
192.6.a.c 1
192.6.a.d 1
192.6.a.e 1
192.6.a.f 1
192.6.a.g 1
192.6.a.h 1
192.6.a.i 1
192.6.a.j 1
192.6.a.k 1
192.6.a.l 1
192.6.a.m 1
192.6.a.n 1
192.6.a.o 1
192.6.a.p 1
192.6.a.q 2
192.6.a.r 2
192.6.c \(\chi_{192}(191, \cdot)\) 192.6.c.a 2 1
192.6.c.b 2
192.6.c.c 2
192.6.c.d 4
192.6.c.e 8
192.6.c.f 20
192.6.d \(\chi_{192}(97, \cdot)\) 192.6.d.a 4 1
192.6.d.b 4
192.6.d.c 4
192.6.d.d 8
192.6.f \(\chi_{192}(95, \cdot)\) 192.6.f.a 4 1
192.6.f.b 4
192.6.f.c 8
192.6.f.d 24
192.6.j \(\chi_{192}(49, \cdot)\) 192.6.j.a 40 2
192.6.k \(\chi_{192}(47, \cdot)\) 192.6.k.a 76 2
192.6.n \(\chi_{192}(25, \cdot)\) None 0 4
192.6.o \(\chi_{192}(23, \cdot)\) None 0 4
192.6.r \(\chi_{192}(13, \cdot)\) n/a 640 8
192.6.s \(\chi_{192}(11, \cdot)\) n/a 1264 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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