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Properties

Label 192.5
Level 192
Weight 5
Dimension 1706
Nonzero newspaces 8
Sturm bound 10240
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(10240\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(192))\).

Total New Old
Modular forms 4240 1750 2490
Cusp forms 3952 1706 2246
Eisenstein series 288 44 244

Trace form

\( 1706 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 10 q^{9} + O(q^{10}) \) \( 1706 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 10 q^{9} - 16 q^{10} + 192 q^{11} - 8 q^{12} + 688 q^{13} - 4 q^{15} - 16 q^{16} - 960 q^{17} - 8 q^{18} - 1420 q^{19} + 28 q^{21} + 5312 q^{22} + 2304 q^{23} + 272 q^{24} - 1458 q^{25} - 10800 q^{26} - 1830 q^{27} - 11296 q^{28} - 3456 q^{29} - 4728 q^{30} + 8 q^{31} + 5040 q^{32} + 4124 q^{33} + 14144 q^{34} + 5184 q^{35} + 18792 q^{36} + 7280 q^{37} + 15120 q^{38} - 8 q^{39} - 736 q^{40} - 5760 q^{41} - 16288 q^{42} - 5580 q^{43} - 16848 q^{44} - 6636 q^{45} - 16 q^{46} - 8 q^{48} + 4774 q^{49} - 43056 q^{50} + 26872 q^{51} - 17968 q^{52} + 3880 q^{54} - 58896 q^{55} + 49392 q^{56} - 5420 q^{57} + 65504 q^{58} - 65280 q^{59} + 31960 q^{60} - 16 q^{61} + 11808 q^{62} - 9616 q^{63} - 24400 q^{64} - 6720 q^{65} - 35560 q^{66} + 91508 q^{67} - 53280 q^{68} + 8788 q^{69} - 122320 q^{70} + 119808 q^{71} - 8 q^{72} + 35820 q^{73} - 33264 q^{74} + 19350 q^{75} + 28272 q^{76} + 14400 q^{77} - 4592 q^{78} - 125448 q^{79} + 105264 q^{80} - 25358 q^{81} - 16 q^{82} - 24000 q^{83} + 57896 q^{84} - 38608 q^{85} - 8 q^{87} - 16 q^{88} - 24960 q^{89} + 111592 q^{90} - 24208 q^{91} + 1600 q^{93} - 16 q^{94} - 25984 q^{96} + 36532 q^{97} - 4996 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.5.b \(\chi_{192}(31, \cdot)\) 192.5.b.a 4 1
192.5.b.b 4
192.5.b.c 8
192.5.e \(\chi_{192}(65, \cdot)\) 192.5.e.a 1 1
192.5.e.b 1
192.5.e.c 2
192.5.e.d 2
192.5.e.e 4
192.5.e.f 4
192.5.e.g 8
192.5.e.h 8
192.5.g \(\chi_{192}(127, \cdot)\) 192.5.g.a 2 1
192.5.g.b 2
192.5.g.c 4
192.5.g.d 4
192.5.g.e 4
192.5.h \(\chi_{192}(161, \cdot)\) 192.5.h.a 4 1
192.5.h.b 4
192.5.h.c 8
192.5.h.d 16
192.5.i \(\chi_{192}(17, \cdot)\) 192.5.i.a 60 2
192.5.l \(\chi_{192}(79, \cdot)\) 192.5.l.a 32 2
192.5.m \(\chi_{192}(7, \cdot)\) None 0 4
192.5.p \(\chi_{192}(41, \cdot)\) None 0 4
192.5.q \(\chi_{192}(5, \cdot)\) n/a 1008 8
192.5.t \(\chi_{192}(19, \cdot)\) n/a 512 8

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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