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 - 12 * q^13 - 8 * q^15 + 6 * q^16 - 2 * q^17 - 10 * q^18 + 4 * q^19 + 24 * q^21 - 6 * q^25 + 8 * q^26 - 4 * q^30 + 2 * q^32 - 24 * q^33 - 18 * q^34 + 4 * q^35 - 2 * q^36 - 8 * q^38 + 24 * q^42 - 40 * q^43 + 32 * q^47 + 2 * q^49 - 2 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 8 * q^55 - 20 * q^59 - 8 * q^60 + 6 * q^64 - 8 * q^67 - 2 * q^68 + 32 * q^69 + 4 * q^70 - 10 * q^72 + 4 * q^76 + 32 * q^77 + 38 * q^81 + 16 * q^83 + 24 * q^84 + 8 * q^85 - 24 * q^86 - 16 * q^87 + 56 * q^93 + 4 * q^94 - 26 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓			170.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+i q^{3}+q^{4}+i q^{5}-i q^{6}+\cdots\)
170.2.b.b	$170$	$2$	170.b	17.b	$2$	$2$	$2$	$1.357$	\(\Q(\sqrt{-1}) \)	None		✓			170.2.b.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+3 i q^{3}+q^{4}+i q^{5}+3 i q^{6}+\cdots\)
170.2.b.c	$170$	$2$	170.b	17.b	$2$	$2$	$2$	$1.357$	\(\Q(\sqrt{-1}) \)	None		✓			170.2.b.c	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+i q^{5}+2 i q^{7}+q^{8}+\cdots\)

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

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