Space of modular forms of level 353, weight 2, and Character 353.c

• Label: 353.2.c
• Level: $353$
• Weight: $2$
• Character orbit: 353.c
• Rep. character: $\chi_{353}(42,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $59$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	353.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 353 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(59\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(353, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	56	56	0
Eisenstein series	4	4	0

Trace form

\( 56 q - 2 q^{3} + 48 q^{4} - 10 q^{5} + 2 q^{6} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(353, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
353.2.c.a	$353$	$2$	353.c	353.c	$4$	$2$	$1$	$2.819$	\(\Q(\sqrt{-1}) \)	None		✓	353.2.c.a	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+q^{2}-q^{4}+(-1-i)q^{5}+(2-2i)q^{7}+\cdots\)
353.2.c.b	$353$	$2$	353.c	353.c	$4$	$8$	$4$	$2.819$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	353.2.c.b	$2$	$0$	\(0\)	\(2\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}-2q^{4}+(\beta _{1}-\beta _{4}+\beta _{5})q^{5}+\cdots\)
353.2.c.c	$353$	$2$	353.c	353.c	$4$	$46$	$23$	$2.819$		None		✓	353.2.c.c	$2$	$0$	\(-2\)	\(-4\)	\(-14\)	\(-2\)		$\mathrm{SU}(2)[C_{4}]$