Space of modular forms of level 161, weight 2, and Character 161.m

• Label: 161.2.m
• Level: $161$
• Weight: $2$
• Character orbit: 161.m
• Rep. character: $\chi_{161}(2,\cdot)$
• Character field: $\Q(\zeta_{33})$
• Dimension: $280$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.m (of order \(33\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{33})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(161, [\chi])\).

	Total	New	Old
Modular forms	360	360	0
Cusp forms	280	280	0
Eisenstein series	80	80	0

Trace form

\( 280 q - 11 q^{2} - 9 q^{3} + q^{4} - 11 q^{5} - 52 q^{6} - 20 q^{7} - 32 q^{8} + 5 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(161, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
161.2.m.a	$161$	$2$	161.m	161.m	$33$	$280$	$14$	$1.286$		None		$4$	$0$	\(-11\)	\(-9\)	\(-11\)	\(-20\)		$\mathrm{SU}(2)[C_{33}]$