LMFDB - Space of Modular Forms of Level 4000, Weight 1, and Character 4000.bf

Defining parameters

The following table gives the dimensions of various subspaces of $M_{1}(4000, [\chi])$.

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	0	0	0	16

Label	Dim.	$A$	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	$A$	Field	Image	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
4000.1.bf.a	$8$	$1.996$	$\Q(\zeta_{20})$	$A_{5}$	None	None	$0$	$-2$	$0$	$4$	$q-\zeta_{20}^{2}q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6})q^{7}+\cdots$
4000.1.bf.b	$8$	$1.996$	$\Q(\zeta_{20})$	$A_{5}$	None	None	$0$	$2$	$0$	$-4$	$q+\zeta_{20}^{2}q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{7}+(-\zeta_{20}^{3}+\cdots)q^{13}+\cdots$

$ S_{1}^{\mathrm{old}}(4000, [\chi]) \cong $ $S_{1}^{\mathrm{new}}(400, [\chi])$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(500, [\chi])$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(2000, [\chi])$$^{\oplus 2}$

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Label	Dim.	\(A\)	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	Image	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
4000.1.bf.a	\(8\)	\(1.996\)	\(\Q(\zeta_{20})\)	\(A_{5}\)	None	None	\(0\)	\(-2\)	\(0\)	\(4\)	\(q-\zeta_{20}^{2}q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6})q^{7}+\cdots\)
4000.1.bf.b	\(8\)	\(1.996\)	\(\Q(\zeta_{20})\)	\(A_{5}\)	None	None	\(0\)	\(2\)	\(0\)	\(-4\)	\(q+\zeta_{20}^{2}q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{7}+(-\zeta_{20}^{3}+\cdots)q^{13}+\cdots\)