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

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

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.t.a \(256\) \(5.232\) None \(0\) \(0\) \(0\) \(0\)

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

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