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Properties

Label 192.11
Level 192
Weight 11
Dimension 4298
Nonzero newspaces 8
Sturm bound 22528
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(22528\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(192))\).

Total New Old
Modular forms 10384 4342 6042
Cusp forms 10096 4298 5798
Eisenstein series 288 44 244

Trace form

\( 4298 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 10 q^{9} + O(q^{10}) \) \( 4298 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 10 q^{9} - 16 q^{10} - 91808 q^{11} - 8 q^{12} - 557744 q^{13} - 4 q^{15} - 16 q^{16} + 3623072 q^{17} - 8 q^{18} - 10214092 q^{19} + 7347340 q^{21} + 17370560 q^{22} - 16559488 q^{23} + 92413712 q^{24} + 31347102 q^{25} - 195998000 q^{26} - 25989654 q^{27} + 71704544 q^{28} + 118609216 q^{29} + 282292872 q^{30} + 8 q^{31} - 368701520 q^{32} - 217732084 q^{33} - 331581376 q^{34} + 68411424 q^{35} + 811717992 q^{36} + 378472496 q^{37} + 303212560 q^{38} - 8 q^{39} - 1839744736 q^{40} - 414977600 q^{41} + 993912032 q^{42} + 376781844 q^{43} - 1807214032 q^{44} + 626733060 q^{45} - 16 q^{46} - 8 q^{48} + 564950470 q^{49} + 4237196496 q^{50} - 2166566024 q^{51} - 5333612080 q^{52} - 382637528 q^{54} - 7135512336 q^{55} + 9214269680 q^{56} - 2515609244 q^{57} + 2649884384 q^{58} + 7495427200 q^{59} - 9129669416 q^{60} - 16 q^{61} - 6642753504 q^{62} - 1129901008 q^{63} + 15115911344 q^{64} - 276186528 q^{65} + 14444806040 q^{66} - 26630064460 q^{67} + 1090322400 q^{68} - 990861404 q^{69} - 39171873232 q^{70} + 45437329920 q^{71} - 8 q^{72} + 3882710508 q^{73} + 22843750160 q^{74} - 35530412346 q^{75} + 47320673904 q^{76} - 13554771936 q^{77} - 30634137200 q^{78} + 62244857592 q^{79} - 1325444304 q^{80} + 1502402674 q^{81} - 16 q^{82} + 14192131360 q^{83} - 9741060568 q^{84} - 4198388848 q^{85} - 8 q^{87} - 16 q^{88} - 14341374400 q^{89} - 42482250008 q^{90} + 12228232112 q^{91} + 2421486880 q^{93} - 16 q^{94} + 55375300736 q^{96} - 69244883756 q^{97} + 33238704572 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.11.b \(\chi_{192}(31, \cdot)\) 192.11.b.a 12 1
192.11.b.b 12
192.11.b.c 16
192.11.e \(\chi_{192}(65, \cdot)\) 192.11.e.a 1 1
192.11.e.b 1
192.11.e.c 2
192.11.e.d 2
192.11.e.e 2
192.11.e.f 2
192.11.e.g 4
192.11.e.h 4
192.11.e.i 10
192.11.e.j 10
192.11.e.k 20
192.11.e.l 20
192.11.g \(\chi_{192}(127, \cdot)\) 192.11.g.a 2 1
192.11.g.b 4
192.11.g.c 4
192.11.g.d 8
192.11.g.e 10
192.11.g.f 12
192.11.h \(\chi_{192}(161, \cdot)\) 192.11.h.a 4 1
192.11.h.b 4
192.11.h.c 24
192.11.h.d 48
192.11.i \(\chi_{192}(17, \cdot)\) n/a 156 2
192.11.l \(\chi_{192}(79, \cdot)\) 192.11.l.a 80 2
192.11.m \(\chi_{192}(7, \cdot)\) None 0 4
192.11.p \(\chi_{192}(41, \cdot)\) None 0 4
192.11.q \(\chi_{192}(5, \cdot)\) n/a 2544 8
192.11.t \(\chi_{192}(19, \cdot)\) n/a 1280 8

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

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(192)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)