Space of modular forms of level 174, weight 2, and Character 174.g

• Label: 174.2.g
• Level: $174$
• Weight: $2$
• Character orbit: 174.g
• Rep. character: $\chi_{174}(7,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 174 = 2 \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	174.g (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(174, [\chi])\).

	Total	New	Old
Modular forms	204	24	180
Cusp forms	156	24	132
Eisenstein series	48	0	48

Trace form

24 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 4 * q^7 + 2 * q^8 - 4 * q^9 + 8 * q^10 - 12 * q^13 + 8 * q^14 - 2 * q^15 - 4 * q^16 + 20 * q^17 + 2 * q^18 + 16 * q^19 - 10 * q^20 - 12 * q^22 + 4 * q^23 + 2 * q^24 - 38 * q^25 - 22 * q^26 + 4 * q^28 - 26 * q^29 - 24 * q^30 - 12 * q^31 + 2 * q^32 + 24 * q^33 - 6 * q^34 - 40 * q^35 - 4 * q^36 - 60 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 + 52 * q^41 + 16 * q^42 + 28 * q^43 - 10 * q^45 + 16 * q^46 - 28 * q^47 + 28 * q^49 - 10 * q^50 - 36 * q^51 + 16 * q^52 - 10 * q^53 + 2 * q^54 + 30 * q^55 + 8 * q^56 - 8 * q^57 + 32 * q^59 - 2 * q^60 - 32 * q^61 + 12 * q^62 - 10 * q^63 - 4 * q^64 - 6 * q^65 + 16 * q^66 - 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^70 - 56 * q^71 + 2 * q^72 + 38 * q^73 + 32 * q^74 + 32 * q^75 - 12 * q^76 - 32 * q^77 + 12 * q^78 + 32 * q^79 + 4 * q^80 - 4 * q^81 - 20 * q^82 + 12 * q^83 - 36 * q^85 + 24 * q^86 + 2 * q^87 - 12 * q^88 + 48 * q^89 + 8 * q^90 + 52 * q^91 + 4 * q^92 + 28 * q^93 + 24 * q^94 + 96 * q^95 + 2 * q^96 + 38 * q^97 - 30 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(174, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
174.2.g.a	$174$	$2$	174.g	29.d	$7$	$6$	$1$	$1.389$	\(\Q(\zeta_{14})\)	None		✓			174.2.g.a	$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\cdots)q^{3}+\cdots\)
174.2.g.b	$174$	$2$	174.g	29.d	$7$	$6$	$1$	$1.389$	\(\Q(\zeta_{14})\)	None		✓			174.2.g.b	$2$	$0$	\(1\)	\(1\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q-\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\cdots)q^{3}+\cdots\)
174.2.g.c	$174$	$2$	174.g	29.d	$7$	$12$	$2$	$1.389$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		174.2.g.c	$2$	$0$	\(2\)	\(-2\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+\beta _{8}q^{2}+\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(174, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(174, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)