LMFDB - Space of modular forms of level 2520, weight 1, and Character 2520.h

Defining parameters

The following table gives the dimensions of various subspaces of $M_{1}(2520, [\chi])$.

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	8	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
2520.1.h.a	$1$	$1.258$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-70}) $	$\Q(\sqrt{105}) $	$-1$	$0$	$-1$	$-1$	$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
2520.1.h.b	$1$	$1.258$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-70}) $	$\Q(\sqrt{105}) $	$-1$	$0$	$1$	$1$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
2520.1.h.c	$1$	$1.258$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-70}) $	$\Q(\sqrt{105}) $	$1$	$0$	$-1$	$1$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
2520.1.h.d	$1$	$1.258$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-70}) $	$\Q(\sqrt{105}) $	$1$	$0$	$1$	$-1$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
2520.1.h.e	$4$	$1.258$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$0$	$q+\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\cdots$

$ S_{1}^{\mathrm{old}}(2520, [\chi]) \cong $ $S_{1}^{\mathrm{new}}(280, [\chi])$$^{\oplus 3}$

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Classical	Maass
Hilbert	Bianchi

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
2520.1.h.a	\(1\)	\(1.258\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \)	\(\Q(\sqrt{105}) \)	\(-1\)	\(0\)	\(-1\)	\(-1\)	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
2520.1.h.b	\(1\)	\(1.258\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \)	\(\Q(\sqrt{105}) \)	\(-1\)	\(0\)	\(1\)	\(1\)	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
2520.1.h.c	\(1\)	\(1.258\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \)	\(\Q(\sqrt{105}) \)	\(1\)	\(0\)	\(-1\)	\(1\)	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
2520.1.h.d	\(1\)	\(1.258\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \)	\(\Q(\sqrt{105}) \)	\(1\)	\(0\)	\(1\)	\(-1\)	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
2520.1.h.e	\(4\)	\(1.258\)	\(\Q(\zeta_{8})\)	\(D_{4}\)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\cdots\)