Space of modular forms of level 74, weight 2, and Character 74.h

• Label: 74.2.h
• Level: $74$
• Weight: $2$
• Character orbit: 74.h
• Rep. character: $\chi_{74}(3,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $19$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(19\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(74, [\chi])\).

	Total	New	Old
Modular forms	72	12	60
Cusp forms	48	12	36
Eisenstein series	24	0	24

Trace form

12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(74, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
74.2.h.a	$74$	$2$	74.h	37.h	$18$	$12$	$2$	$0.591$	\(\Q(\zeta_{36})\)	None		✓	✓	✓	74.2.h.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\zeta_{36}q^{2}+(1-\zeta_{36}^{4}-\zeta_{36}^{6})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(74, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)