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

• Label: 74.2.f
• Level: $74$
• Weight: $2$
• Character orbit: 74.f
• Rep. character: $\chi_{74}(7,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $19$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(19\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	66	18	48
Cusp forms	42	18	24
Eisenstein series	24	0	24

Trace form

18 * q - 6 * q^3 - 3 * q^5 + 12 * q^7 - 3 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 - 6 * q^12 - 6 * q^13 + 6 * q^14 - 12 * q^15 - 3 * q^17 + 6 * q^19 - 3 * q^20 - 30 * q^21 - 36 * q^23 + 15 * q^25 - 9 * q^26 + 6 * q^27 - 6 * q^28 + 6 * q^29 + 24 * q^30 + 24 * q^31 + 54 * q^33 - 3 * q^34 - 6 * q^35 + 18 * q^36 + 6 * q^37 + 48 * q^38 - 6 * q^39 + 18 * q^40 - 15 * q^41 - 36 * q^42 + 48 * q^43 - 6 * q^44 - 6 * q^45 + 18 * q^46 + 6 * q^47 - 12 * q^49 + 18 * q^50 + 12 * q^52 - 24 * q^53 - 36 * q^54 - 18 * q^55 - 24 * q^57 - 21 * q^58 - 12 * q^59 - 30 * q^61 - 36 * q^62 + 42 * q^63 - 9 * q^64 + 3 * q^65 - 30 * q^67 - 12 * q^68 + 30 * q^69 - 12 * q^70 - 24 * q^71 + 18 * q^73 + 21 * q^74 - 36 * q^75 + 6 * q^76 + 36 * q^77 - 42 * q^78 + 18 * q^79 - 12 * q^80 - 24 * q^81 - 24 * q^82 - 12 * q^84 - 15 * q^85 + 12 * q^86 + 12 * q^87 + 12 * q^88 - 48 * q^89 - 21 * q^90 - 42 * q^91 + 6 * q^92 + 48 * q^93 - 24 * q^94 + 36 * q^95 + 60 * q^98 - 6 * 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.f.a	$74$	$2$	74.f	37.f	$9$	$6$	$1$	$0.591$	\(\Q(\zeta_{18})\)	None		✓			74.2.f.a	$2$	$0$	\(0\)	\(-3\)	\(3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
74.2.f.b	$74$	$2$	74.f	37.f	$9$	$12$	$2$	$0.591$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		74.2.f.b	$2$	$0$	\(0\)	\(-3\)	\(-6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{4}-\beta _{7})q^{2}+(-1+\beta _{1}-\beta _{8})q^{3}+\cdots\)

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

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