⌂ → Modular forms → Classical → Level 192 → Weight 4 → Character orbit f

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Space of modular forms of level 192, weight 4, and Character 192.f

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Properties

Label	192.4.f

Level	$192$
Weight	$4$
Character orbit	192.f
Rep. character	$\chi_{192}(95,\cdot)$
Character field	$\Q$
Dimension	$24$
Newform subspaces	$4$
Sturm bound	$128$
Trace bound	$15$

Related objects

Newspace 192.4

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Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(192, [\chi])\).

	Total	New	Old
Modular forms	108	24	84
Cusp forms	84	24	60
Eisenstein series	24	0	24

Trace form

Decomposition of \(S_{4}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
192.4.f.a	$192$	$4$	192.f	24.f	$2$	$4$	$4$	$11.328$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-6}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}-17\zeta_{12}q^{7}+\cdots\)
192.4.f.b	$192$	$4$	192.f	24.f	$2$	$4$	$4$	$11.328$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{12}q^{3}-5\zeta_{12}^{2}q^{7}+3^{3}q^{9}+3\zeta_{12}^{3}q^{13}+\cdots\)
192.4.f.c	$192$	$4$	192.f	24.f	$2$	$8$	$8$	$11.328$	8.0.1731891456.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(3\beta _{1}-\beta _{3}+\beta _{5})q^{5}+\beta _{7}q^{7}+\cdots\)
192.4.f.d	$192$	$4$	192.f	24.f	$2$	$8$	$8$	$11.328$	8.0.1731891456.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(3\beta _{1}-\beta _{3}+\beta _{5})q^{5}-\beta _{7}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)