Space of modular forms of level 109, weight 2, and Character 109.b

• Label: 109.2.b
• Level: $109$
• Weight: $2$
• Character orbit: 109.b
• Rep. character: $\chi_{109}(108,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	109.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 109 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(109, [\chi])\).

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

Trace form

\( 8 q - 14 q^{4} + 2 q^{5} - 6 q^{7} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(109, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
109.2.b.a	$109$	$2$	109.b	109.b	$2$	$2$	$2$	$0.870$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(4\)	\(-6\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}+2q^{3}-q^{4}-3q^{5}-2\zeta_{6}q^{6}+\cdots\)
109.2.b.b	$109$	$2$	109.b	109.b	$2$	$6$	$6$	$0.870$	6.0.191244096.1	None		$2$	$0$	\(0\)	\(-4\)	\(8\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(-2-\beta _{3}+\cdots)q^{4}+\cdots\)