Properties

Label 192.3.q
Level $192$
Weight $3$
Character orbit 192.q
Rep. character $\chi_{192}(5,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $496$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 192.q (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).

Total New Old
Modular forms 528 528 0
Cusp forms 496 496 0
Eisenstein series 32 32 0

Trace form

\( 496q - 8q^{3} - 16q^{4} - 8q^{6} - 16q^{7} - 8q^{9} + O(q^{10}) \) \( 496q - 8q^{3} - 16q^{4} - 8q^{6} - 16q^{7} - 8q^{9} - 16q^{10} - 8q^{12} - 16q^{13} - 8q^{15} - 16q^{16} - 8q^{18} - 16q^{19} - 8q^{21} - 16q^{22} + 272q^{24} - 16q^{25} - 8q^{27} - 16q^{28} + 72q^{30} - 16q^{34} - 408q^{36} - 16q^{37} - 8q^{39} - 16q^{40} - 448q^{42} - 16q^{43} - 8q^{45} - 16q^{46} - 8q^{48} - 16q^{49} - 8q^{51} - 544q^{52} - 8q^{54} + 496q^{55} - 8q^{57} - 736q^{58} - 8q^{60} - 16q^{61} - 16q^{63} + 80q^{64} - 40q^{66} - 528q^{67} - 8q^{69} + 656q^{70} - 8q^{72} - 16q^{73} - 8q^{75} + 1440q^{76} - 416q^{78} - 528q^{79} - 8q^{81} - 1056q^{82} - 1240q^{84} - 16q^{85} - 8q^{87} - 576q^{88} - 728q^{90} - 16q^{91} + 64q^{93} - 112q^{94} + 128q^{96} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
192.3.q.a \(496\) \(5.232\) None \(0\) \(-8\) \(0\) \(-16\)