LMFDB - Space of modular forms of level 192, weight 10, and Character 192.f

Defining parameters

The following table gives the dimensions of various subspaces of $M_{10}(192, [\chi])$.

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	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	Twist minimal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
192.10.f.a	$192$	$10$	192.f	24.f	$2$	$4$	$4$	$98.887$	$\Q(\zeta_{12})$	$\Q(\sqrt{-6}) $		✓	192.10.f.a	$8$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-9\zeta_{12}^{2}q^{3}-89\zeta_{12}^{3}q^{5}+2159\zeta_{12}q^{7}+\cdots$
192.10.f.b	$192$	$10$	192.f	24.f	$2$	$4$	$4$	$98.887$	$\Q(\zeta_{12})$	$\Q(\sqrt{-3}) $		✓	192.10.f.b	$8$	$0$	$0$	$0$	$0$	$0$	$2^{6}\cdot 3^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-3\zeta_{12}^{2}q^{3}-3145\zeta_{12}q^{7}+3^{9}q^{9}+\cdots$
192.10.f.c	$192$	$10$	192.f	24.f	$2$	$16$	$16$	$98.887$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	192.10.f.c	$8$	$0$	$0$	$0$	$0$	$0$	$2^{60}\cdot 3^{28}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+\beta _{9}q^{5}+(-504\beta _{4}-7\beta _{7}+\cdots)q^{7}+\cdots$
192.10.f.d	$192$	$10$	192.f	24.f	$2$	$48$	$48$	$98.887$		None		✓	192.10.f.d	$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$

$ S_{10}^{\mathrm{old}}(192, [\chi]) \simeq $ $S_{10}^{\mathrm{new}}(24, [\chi])$$^{\oplus 4}$$\oplus$$S_{10}^{\mathrm{new}}(48, [\chi])$$^{\oplus 3}$$\oplus$$S_{10}^{\mathrm{new}}(96, [\chi])$$^{\oplus 2}$

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