Space of modular forms of level 2180, weight 1, and Character 2180.h

• Label: 2180.1.h
• Level: $2180$
• Weight: $1$
• Character orbit: 2180.h
• Rep. character: $\chi_{2180}(2179,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $8$
• Sturm bound: $330$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2180 = 2^{2} \cdot 5 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2180.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2180 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(330\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2180, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	20	20	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q + 8 q^{4} - 2 q^{5} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2180, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2180.1.h.a	$2180$	$1$	2180.h	2180.h	$2$	$1$	$1$	$1.088$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-545}) \)	\(\Q(\sqrt{545}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{9}-q^{10}+\cdots\)
2180.1.h.b	$2180$	$1$	2180.h	2180.h	$2$	$1$	$1$	$1.088$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-545}) \)	\(\Q(\sqrt{545}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{5}+q^{8}-q^{9}+q^{10}+\cdots\)
2180.1.h.c	$2180$	$1$	2180.h	2180.h	$2$	$2$	$2$	$1.088$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-545}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$		\(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+\beta q^{7}+\cdots\)
2180.1.h.d	$2180$	$1$	2180.h	2180.h	$2$	$2$	$2$	$1.088$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-109}) \)	\(\Q(\sqrt{545}) \)		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-iq^{2}-q^{4}-q^{5}+iq^{8}-q^{9}+iq^{10}+\cdots\)
2180.1.h.e	$2180$	$1$	2180.h	2180.h	$2$	$2$	$2$	$1.088$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-545}) \)	None	✓	$4$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$1$		\(q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+\beta q^{7}+\cdots\)
2180.1.h.f	$2180$	$1$	2180.h	2180.h	$2$	$4$	$4$	$1.088$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-545}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)	$1$		\(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2180.1.h.g	$2180$	$1$	2180.h	2180.h	$2$	$4$	$4$	$1.088$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-109}) \)	None		$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
2180.1.h.h	$2180$	$1$	2180.h	2180.h	$2$	$4$	$4$	$1.088$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-545}) \)	None	✓	$4$	$0$	\(4\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)