LMFDB - Space of modular forms of level 2303, weight 1, and Character 2303.d

Defining parameters

The following table gives the dimensions of various subspaces of $M_{1}(2303, [\chi])$.

The following table gives the dimensions of subspaces with specified projective image type.

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	12	0	0	0

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	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	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
2303.1.d.a	$2303$	$1$	2303.d	47.b	$2$	$1$	$1$	$1.149$	$\Q$	$D_{3}$	$\Q(\sqrt{-47}) $	None	✓				329.1.f.a	$2$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-q^{2}-2q^{3}+2q^{6}+q^{8}+3q^{9}-q^{16}+\cdots$
2303.1.d.b	$2303$	$1$	2303.d	47.b	$2$	$1$	$1$	$1.149$	$\Q$	$D_{3}$	$\Q(\sqrt{-47}) $	None	✓				329.1.f.a	$2$	$0$	$-1$	$2$	$0$	$0$	$1$		$q-q^{2}+2q^{3}-2q^{6}+q^{8}+3q^{9}-q^{16}+\cdots$
2303.1.d.c	$2303$	$1$	2303.d	47.b	$2$	$2$	$2$	$1.149$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-47}) $	None	✓				47.1.b.a	$2$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\beta q^{2}+(1-\beta )q^{3}+\beta q^{4}+q^{6}-q^{8}+\cdots$
2303.1.d.d	$2303$	$1$	2303.d	47.b	$2$	$4$	$4$	$1.149$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-47}) $	None	✓				329.1.f.b	$2$	$0$	$1$	$-2$	$0$	$0$	$1$		$q+(1-\beta _{1}+\beta _{3})q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
2303.1.d.e	$2303$	$1$	2303.d	47.b	$2$	$4$	$4$	$1.149$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-47}) $	None	✓				329.1.f.b	$2$	$0$	$1$	$2$	$0$	$0$	$1$		$q+(1-\beta _{1}+\beta _{3})q^{2}-\beta _{3}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$

$ S_{1}^{\mathrm{old}}(2303, [\chi]) \simeq $ $S_{1}^{\mathrm{new}}(47, [\chi])$$^{\oplus 3}$

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