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

• Label: 170.2.n
• Level: $170$
• Weight: $2$
• Character orbit: 170.n
• Rep. character: $\chi_{170}(9,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $54$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(54\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	120	40	80
Cusp forms	88	40	48
Eisenstein series	32	0	32

Trace form

\( 40 q - 8 q^{5} + O(q^{10}) \)

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.n.a	$170$	$2$	170.n	85.m	$8$	$20$	$5$	$1.357$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{8}]$	\(q+\beta _{7}q^{2}-\beta _{6}q^{3}-\beta _{10}q^{4}+\beta _{14}q^{5}+\cdots\)
170.2.n.b	$170$	$2$	170.n	85.m	$8$	$20$	$5$	$1.357$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{8}]$	\(q+\beta _{8}q^{2}+\beta _{5}q^{3}+\beta _{10}q^{4}-\beta _{16}q^{5}+\cdots\)

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

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