Properties

Label 192.2
Level 192
Weight 2
Dimension 410
Nonzero newspaces 8
Newform subspaces 13
Sturm bound 4096
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 13 \)
Sturm bound: \(4096\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(192))\).

Total New Old
Modular forms 1168 454 714
Cusp forms 881 410 471
Eisenstein series 287 44 243

Trace form

\( 410q - 6q^{3} - 16q^{4} - 8q^{6} - 8q^{7} - 10q^{9} + O(q^{10}) \) \( 410q - 6q^{3} - 16q^{4} - 8q^{6} - 8q^{7} - 10q^{9} - 16q^{10} + 8q^{11} - 8q^{12} - 16q^{16} + 16q^{17} - 8q^{18} + 4q^{19} - 12q^{21} - 32q^{22} - 48q^{24} - 42q^{25} - 80q^{26} - 18q^{27} - 96q^{28} - 32q^{29} - 88q^{30} - 56q^{31} - 80q^{32} - 44q^{33} - 96q^{34} - 24q^{35} - 88q^{36} - 48q^{37} - 80q^{38} - 28q^{39} - 96q^{40} - 32q^{41} - 48q^{42} - 20q^{43} - 16q^{44} - 52q^{45} - 16q^{46} - 8q^{48} - 42q^{49} + 48q^{50} - 72q^{51} + 80q^{52} + 8q^{54} - 168q^{55} + 112q^{56} - 36q^{57} + 128q^{58} - 160q^{59} + 88q^{60} - 16q^{61} + 96q^{62} - 40q^{63} + 176q^{64} - 16q^{65} + 72q^{66} - 188q^{67} + 96q^{68} + 28q^{69} + 176q^{70} - 128q^{71} - 8q^{72} - 20q^{73} + 112q^{74} - 54q^{75} + 112q^{76} + 48q^{77} + 64q^{78} - 56q^{79} + 48q^{80} + 50q^{81} - 16q^{82} + 40q^{83} + 104q^{84} + 32q^{85} + 52q^{87} - 16q^{88} + 32q^{89} + 136q^{90} + 48q^{91} + 48q^{93} - 16q^{94} + 48q^{95} + 128q^{96} + 36q^{97} + 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.2.a \(\chi_{192}(1, \cdot)\) 192.2.a.a 1 1
192.2.a.b 1
192.2.a.c 1
192.2.a.d 1
192.2.c \(\chi_{192}(191, \cdot)\) 192.2.c.a 2 1
192.2.c.b 4
192.2.d \(\chi_{192}(97, \cdot)\) 192.2.d.a 4 1
192.2.f \(\chi_{192}(95, \cdot)\) 192.2.f.a 4 1
192.2.f.b 4
192.2.j \(\chi_{192}(49, \cdot)\) 192.2.j.a 8 2
192.2.k \(\chi_{192}(47, \cdot)\) 192.2.k.a 12 2
192.2.n \(\chi_{192}(25, \cdot)\) None 0 4
192.2.o \(\chi_{192}(23, \cdot)\) None 0 4
192.2.r \(\chi_{192}(13, \cdot)\) 192.2.r.a 128 8
192.2.s \(\chi_{192}(11, \cdot)\) 192.2.s.a 240 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

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