Space of modular forms of level 1480, weight 1, and Character 1480.h

• Label: 1480.1.h
• Level: $1480$
• Weight: $1$
• Character orbit: 1480.h
• Rep. character: $\chi_{1480}(739,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $6$
• Sturm bound: $228$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1480 = 2^{3} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1480.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1480 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(228\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1480, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	14	14	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	14	0	0	0

Trace form

\( 14 q - 6 q^{4} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1480, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1480.1.h.a	$1480$	$1$	1480.h	1480.h	$2$	$1$	$1$	$0.739$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-370}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{9}+\cdots\)
1480.1.h.b	$1480$	$1$	1480.h	1480.h	$2$	$1$	$1$	$0.739$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-370}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)	$1$		\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}+q^{9}+\cdots\)
1480.1.h.c	$1480$	$1$	1480.h	1480.h	$2$	$1$	$1$	$0.739$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-370}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)	$1$		\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}+q^{9}+\cdots\)
1480.1.h.d	$1480$	$1$	1480.h	1480.h	$2$	$1$	$1$	$0.739$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-370}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{9}+\cdots\)
1480.1.h.e	$1480$	$1$	1480.h	1480.h	$2$	$2$	$2$	$0.739$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-74}) \)	\(\Q(\sqrt{185}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-q^{4}-iq^{5}+iq^{8}+q^{9}-q^{10}+\cdots\)
1480.1.h.f	$1480$	$1$	1480.h	1480.h	$2$	$8$	$8$	$0.739$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-74}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{20}^{5}q^{2}+(\zeta_{20}^{2}+\zeta_{20}^{8})q^{3}-q^{4}+\cdots\)