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

• Label: 170.2.c
• Level: $170$
• Weight: $2$
• Character orbit: 170.c
• Rep. character: $\chi_{170}(69,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $54$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	32	8	24
Cusp forms	24	8	16
Eisenstein series	8	0	8

Trace form

\( 8 q - 8 q^{4} + 4 q^{5} - 12 q^{9} + O(q^{10}) \)

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.c.a	$170$	$2$	170.c	5.b	$2$	$2$	$2$	$1.357$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}-q^{6}+\cdots\)
170.2.c.b	$170$	$2$	170.c	5.b	$2$	$6$	$6$	$1.357$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}-q^{4}+\cdots\)

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

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