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Properties

Label 192.9
Level 192
Weight 9
Dimension 3434
Nonzero newspaces 8
Sturm bound 18432
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(18432\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(192))\).

Total New Old
Modular forms 8336 3478 4858
Cusp forms 8048 3434 4614
Eisenstein series 288 44 244

Trace form

\( 3434 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 10 q^{9} + O(q^{10}) \) \( 3434 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 10 q^{9} - 16 q^{10} - 39552 q^{11} - 8 q^{12} + 102768 q^{13} - 4 q^{15} - 16 q^{16} - 309120 q^{17} - 8 q^{18} + 335092 q^{19} + 269884 q^{21} + 2136512 q^{22} - 1691136 q^{23} - 322288 q^{24} + 3614382 q^{25} + 6728400 q^{26} + 25530 q^{27} - 7230496 q^{28} - 4264704 q^{29} - 7934328 q^{30} + 8 q^{31} + 9681840 q^{32} + 6623804 q^{33} + 16553024 q^{34} + 2415744 q^{35} - 7200408 q^{36} - 9441040 q^{37} - 32644080 q^{38} - 8 q^{39} + 2303264 q^{40} + 17498880 q^{41} + 35148512 q^{42} + 1859700 q^{43} - 45304272 q^{44} - 15374796 q^{45} - 16 q^{46} - 8 q^{48} + 11529574 q^{49} + 10290384 q^{50} - 54228488 q^{51} + 91896272 q^{52} - 19840472 q^{54} + 231633904 q^{55} - 113749776 q^{56} - 11029580 q^{57} + 101752544 q^{58} - 224693760 q^{59} + 163708120 q^{60} - 16 q^{61} + 87863328 q^{62} - 23059216 q^{63} - 193535824 q^{64} + 120408960 q^{65} - 227317864 q^{66} + 492471028 q^{67} - 163729440 q^{68} - 73697612 q^{69} + 185779760 q^{70} - 478992384 q^{71} - 8 q^{72} - 95283220 q^{73} + 340057872 q^{74} + 35256630 q^{75} - 318607760 q^{76} + 153244800 q^{77} - 667571312 q^{78} + 361016312 q^{79} + 404319024 q^{80} + 62519794 q^{81} - 16 q^{82} - 209328000 q^{83} - 689231320 q^{84} - 135303568 q^{85} - 8 q^{87} - 16 q^{88} + 243559680 q^{89} + 873269992 q^{90} + 197542640 q^{91} + 184082560 q^{93} - 16 q^{94} - 468840832 q^{96} - 54952588 q^{97} - 315415300 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(192))\)

We only show spaces with odd 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
192.9.b \(\chi_{192}(31, \cdot)\) 192.9.b.a 8 1
192.9.b.b 12
192.9.b.c 12
192.9.e \(\chi_{192}(65, \cdot)\) 192.9.e.a 1 1
192.9.e.b 1
192.9.e.c 2
192.9.e.d 2
192.9.e.e 2
192.9.e.f 2
192.9.e.g 2
192.9.e.h 2
192.9.e.i 8
192.9.e.j 8
192.9.e.k 16
192.9.e.l 16
192.9.g \(\chi_{192}(127, \cdot)\) 192.9.g.a 2 1
192.9.g.b 2
192.9.g.c 4
192.9.g.d 8
192.9.g.e 8
192.9.g.f 8
192.9.h \(\chi_{192}(161, \cdot)\) 192.9.h.a 4 1
192.9.h.b 4
192.9.h.c 16
192.9.h.d 40
192.9.i \(\chi_{192}(17, \cdot)\) n/a 124 2
192.9.l \(\chi_{192}(79, \cdot)\) 192.9.l.a 64 2
192.9.m \(\chi_{192}(7, \cdot)\) None 0 4
192.9.p \(\chi_{192}(41, \cdot)\) None 0 4
192.9.q \(\chi_{192}(5, \cdot)\) n/a 2032 8
192.9.t \(\chi_{192}(19, \cdot)\) n/a 1024 8

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(192)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)