Space of modular forms of level 170, weight 2, and Character 170.b

• Label: 170.2.b
• Level: $170$
• Weight: $2$
• Character orbit: 170.b
• Rep. character: $\chi_{170}(101,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $54$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(54\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(170, [\chi])\).

	Total	New	Old
Modular forms	30	6	24
Cusp forms	22	6	16
Eisenstein series	8	0	8

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(170, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
170.2.b.a	$170$	$2$	170.b	17.b	$2$	$2$	$2$	$1.357$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+iq^{3}+q^{4}+iq^{5}-iq^{6}-q^{8}+\cdots\)
170.2.b.b	$170$	$2$	170.b	17.b	$2$	$2$	$2$	$1.357$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+3iq^{3}+q^{4}+iq^{5}+3iq^{6}+\cdots\)
170.2.b.c	$170$	$2$	170.b	17.b	$2$	$2$	$2$	$1.357$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+iq^{5}+2iq^{7}+q^{8}+3q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)