Space of modular forms of level 10, weight 3, and Character 10.c

• Label: 10.3.c
• Level: $10$
• Weight: $3$
• Character orbit: 10.c
• Rep. character: $\chi_{10}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(10, [\chi])\).

	Total	New	Old
Modular forms	10	2	8
Cusp forms	2	2	0
Eisenstein series	8	0	8

Trace form

\( 2 q - 2 q^{2} - 4 q^{3} + 8 q^{6} + 4 q^{7} + 4 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.3.c.a	$10$	$3$	10.c	5.c	$4$	$2$	$1$	$0.272$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(-4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)