Space of modular forms of level 354, weight 2, and Character 354.c

• Label: 354.2.c
• Level: $354$
• Weight: $2$
• Character orbit: 354.c
• Rep. character: $\chi_{354}(353,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 177 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(354, [\chi])\).

	Total	New	Old
Modular forms	64	20	44
Cusp forms	56	20	36
Eisenstein series	8	0	8

Trace form

\( 20 q - 2 q^{3} + 20 q^{4} - 4 q^{7} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(354, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
354.2.c.a	$354$	$2$	354.c	177.d	$2$	$10$	$10$	$2.827$	10.0.\(\cdots\).1	None		$2$	$0$	\(-10\)	\(-1\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)
354.2.c.b	$354$	$2$	354.c	177.d	$2$	$10$	$10$	$2.827$	10.0.\(\cdots\).1	None		$2$	$0$	\(10\)	\(-1\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(354, [\chi]) \cong \)