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

• Label: 174.2.d
• Level: $174$
• Weight: $2$
• Character orbit: 174.d
• Rep. character: $\chi_{174}(115,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 174 = 2 \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	174.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	34	6	28
Cusp forms	26	6	20
Eisenstein series	8	0	8

Trace form

6 * q - 6 * q^4 - 2 * q^6 + 4 * q^7 - 6 * q^9 + 4 * q^13 + 6 * q^16 - 16 * q^22 + 2 * q^24 + 6 * q^25 - 4 * q^28 - 20 * q^29 + 4 * q^30 - 16 * q^33 - 16 * q^34 + 40 * q^35 + 6 * q^36 + 16 * q^38 + 8 * q^42 + 10 * q^49 - 4 * q^51 - 4 * q^52 + 8 * q^53 + 2 * q^54 + 12 * q^57 + 6 * q^58 - 12 * q^59 + 12 * q^62 - 4 * q^63 - 6 * q^64 - 56 * q^65 - 8 * q^67 - 8 * q^71 + 4 * q^74 + 12 * q^78 + 6 * q^81 + 28 * q^83 - 8 * q^86 + 14 * q^87 + 16 * q^88 - 40 * q^91 - 28 * q^93 - 4 * q^94 - 2 * q^96

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.d.a	$174$	$2$	174.d	29.b	$2$	$2$	$2$	$1.389$	\(\Q(\sqrt{-1}) \)	None		✓			174.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{5}+q^{6}+\cdots\)
174.2.d.b	$174$	$2$	174.d	29.b	$2$	$4$	$4$	$1.389$	\(\Q(i, \sqrt{33})\)	None		✓	✓		174.2.d.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+(-1+\beta _{3})q^{5}+\cdots\)

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

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