Space of modular forms of level 484, weight 1, and Character 484.h

• Label: 484.1.h
• Level: $484$
• Weight: $1$
• Character orbit: 484.h
• Rep. character: $\chi_{484}(3,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $66$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	484.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(66\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(484, [\chi])\).

	Total	New	Old
Modular forms	56	40	16
Cusp forms	8	8	0
Eisenstein series	48	32	16

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

Trace form

\( 8 q - 2 q^{4} + 2 q^{5} - 2 q^{9} - 2 q^{16} + 2 q^{20} + 2 q^{26} - 8 q^{34} - 2 q^{36} + 2 q^{37} - 8 q^{45} - 2 q^{49} + 2 q^{53} + 2 q^{58} - 2 q^{64} + 2 q^{80} - 2 q^{81} + 2 q^{82} - 8 q^{89} + 2 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(484, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
484.1.h.a	$484$	$1$	484.h	44.h	$10$	$4$	$1$	$0.242$	\(\Q(\zeta_{10})\)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		✓			484.1.b.a	$8$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}-\zeta_{10}^{3}q^{8}+\cdots\)
484.1.h.b	$484$	$1$	484.h	44.h	$10$	$4$	$1$	$0.242$	\(\Q(\zeta_{10})\)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		✓			484.1.b.a	$8$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+\zeta_{10}^{3}q^{8}+\cdots\)