Space of modular forms of level 1476, weight 1, and Character 1476.cc

• Label: 1476.1.cc
• Level: $1476$
• Weight: $1$
• Character orbit: 1476.cc
• Rep. character: $\chi_{1476}(35,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $252$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1476.cc (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 492 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(252\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1476, [\chi])\).

	Total	New	Old
Modular forms	160	32	128
Cusp forms	32	32	0
Eisenstein series	128	0	128

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1476, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1476.1.cc.a	$1476$	$1$	1476.cc	492.ae	$40$	$16$	$1$	$0.737$	\(\Q(\zeta_{40})\)	$D_{40}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(\zeta_{40}^{8}+\zeta_{40}^{14}+\cdots)q^{5}+\cdots\)
1476.1.cc.b	$1476$	$1$	1476.cc	492.ae	$40$	$16$	$1$	$0.737$	\(\Q(\zeta_{40})\)	$D_{40}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(-\zeta_{40}^{8}+\cdots)q^{5}+\cdots\)