Properties

Label 192.3.t
Level $192$
Weight $3$
Character orbit 192.t
Rep. character $\chi_{192}(19,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $256$
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.t (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
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 528 256 272
Cusp forms 496 256 240
Eisenstein series 32 0 32

Trace form

\( 256 q + O(q^{10}) \) \( 256 q + 144 q^{22} + 400 q^{26} + 240 q^{28} - 80 q^{32} - 240 q^{34} - 560 q^{38} - 720 q^{40} - 208 q^{44} - 624 q^{50} + 384 q^{51} - 528 q^{52} - 144 q^{54} + 512 q^{55} - 784 q^{56} + 512 q^{59} - 288 q^{60} - 96 q^{62} + 96 q^{64} + 288 q^{66} - 128 q^{67} + 480 q^{68} + 672 q^{70} - 1024 q^{71} + 1232 q^{74} - 768 q^{75} + 208 q^{76} + 720 q^{78} - 512 q^{79} + 816 q^{80} + 1040 q^{82} + 560 q^{88} + 96 q^{94} + O(q^{100}) \)

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.t.a 192.t 64.j $256$ $5.232$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)