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

• Label: 74.2.e
• Level: $74$
• Weight: $2$
• Character orbit: 74.e
• Rep. character: $\chi_{74}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $19$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(19\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	24	8	16
Cusp forms	16	8	8
Eisenstein series	8	0	8

Trace form

8 * q - 4 * q^3 + 4 * q^4 - 4 * q^7 - 4 * q^9 + 4 * q^12 - 12 * q^13 - 4 * q^16 - 4 * q^21 - 8 * q^25 - 24 * q^26 + 32 * q^27 + 4 * q^28 - 12 * q^30 + 12 * q^33 + 12 * q^34 + 36 * q^35 - 8 * q^36 - 4 * q^37 - 24 * q^39 + 36 * q^42 + 12 * q^46 + 24 * q^47 + 8 * q^48 - 12 * q^49 - 12 * q^52 - 36 * q^55 - 36 * q^57 - 12 * q^58 + 36 * q^61 - 12 * q^62 + 8 * q^63 - 8 * q^64 - 12 * q^65 + 8 * q^67 - 12 * q^71 + 8 * q^73 - 24 * q^74 + 16 * q^75 - 36 * q^77 + 24 * q^78 - 12 * q^79 - 4 * q^81 - 12 * q^83 - 8 * q^84 + 24 * q^85 + 24 * q^86 - 72 * q^87 + 36 * q^89 - 24 * q^90 - 24 * q^91 - 12 * q^93 + 36 * q^94 - 12 * q^95 + 24 * 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.e.a	$74$	$2$	74.e	37.e	$6$	$4$	$2$	$0.591$	\(\Q(\zeta_{12})\)	None		✓			74.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(-6\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
74.2.e.b	$74$	$2$	74.e	37.e	$6$	$4$	$2$	$0.591$	\(\Q(\zeta_{12})\)	None		✓			74.2.e.b	$2$	$0$	\(0\)	\(-2\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)

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

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