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

• Label: 74.2.c
• Level: $74$
• Weight: $2$
• Character orbit: 74.c
• Rep. character: $\chi_{74}(47,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $19$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	22	10	12
Cusp forms	14	10	4
Eisenstein series	8	0	8

Trace form

10 * q - q^2 - 5 * q^4 - 3 * q^5 + 4 * q^7 + 2 * q^8 - 9 * q^9 - 2 * q^10 - 2 * q^13 + 8 * q^14 + 4 * q^15 - 5 * q^16 - 3 * q^17 - 5 * q^18 - 12 * q^19 - 3 * q^20 + 8 * q^21 - 8 * q^22 + 16 * q^23 - 20 * q^25 + 20 * q^26 - 24 * q^27 + 4 * q^28 - 18 * q^29 - 12 * q^30 + 32 * q^31 - q^32 - 4 * q^33 + 9 * q^34 + 16 * q^35 + 18 * q^36 - q^37 + 8 * q^38 + 16 * q^39 + q^40 + q^41 + 24 * q^42 - 8 * q^43 + 70 * q^45 - 8 * q^46 - 40 * q^47 + 3 * q^49 - 20 * q^50 - 64 * q^51 - 2 * q^52 - 10 * q^53 + 12 * q^54 - 12 * q^55 - 4 * q^56 + 20 * q^57 - 3 * q^58 - 12 * q^59 - 8 * q^60 - 3 * q^61 + 8 * q^62 + 16 * q^63 + 10 * q^64 - 14 * q^65 - 56 * q^66 + 20 * q^67 + 6 * q^68 + 28 * q^69 - 8 * q^70 + 24 * q^71 - 5 * q^72 - 20 * q^73 + 18 * q^74 + 56 * q^75 - 12 * q^76 - 36 * q^77 - 16 * q^78 - 16 * q^79 + 6 * q^80 + 11 * q^81 - 26 * q^82 - 12 * q^83 - 16 * q^84 - 6 * q^85 - 20 * q^86 + 8 * q^87 + 16 * q^88 + q^89 - 31 * q^90 + 8 * q^91 - 8 * q^92 - 36 * q^93 + 12 * q^94 + 32 * q^95 + 6 * q^97 + 7 * q^98 - 48 * 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.c.a	$74$	$2$	74.c	37.c	$3$	$2$	$1$	$0.591$	\(\Q(\sqrt{-3}) \)	None		✓			74.2.c.a	$2$	$0$	\(1\)	\(-2\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
74.2.c.b	$74$	$2$	74.c	37.c	$3$	$2$	$1$	$0.591$	\(\Q(\sqrt{-3}) \)	None		✓			74.2.c.b	$2$	$0$	\(1\)	\(2\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+2\zeta_{6}q^{3}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
74.2.c.c	$74$	$2$	74.c	37.c	$3$	$6$	$3$	$0.591$	6.0.4406832.1	None		✓	✓		74.2.c.c	$2$	$0$	\(-3\)	\(0\)	\(-1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{3})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\beta _{3}q^{4}+\cdots\)

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

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