LMFDB - Space of modular forms of level 3528, weight 1, and Character 3528.bw

Defining parameters

The following table gives the dimensions of various subspaces of $M_{1}(3528, [\chi])$.

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	10	0	0	0

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
3528.1.bw.a	$2$	$1.761$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	$-1$	$0$	$0$	$0$	$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots$
3528.1.bw.b	$4$	$1.761$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{42}) $	$0$	$0$	$0$	$0$	$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots$
3528.1.bw.c	$4$	$1.761$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$0$	$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots$

$ S_{1}^{\mathrm{old}}(3528, [\chi]) \cong $ $S_{1}^{\mathrm{new}}(392, [\chi])$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(504, [\chi])$$^{\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
3528.1.bw.a	\(2\)	\(1.761\)	\(\Q(\sqrt{-3}) \)	\(D_{2}\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)	\(-1\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots\)
3528.1.bw.b	\(4\)	\(1.761\)	\(\Q(\zeta_{12})\)	\(D_{2}\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{42}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots\)
3528.1.bw.c	\(4\)	\(1.761\)	\(\Q(\zeta_{12})\)	\(D_{6}\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)