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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 $0$

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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.3.q.a 192.q 192.q $496$ $5.232$ None \(0\) \(-8\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{16}]$