Space of modular forms of level 742, weight 2, and Character 742.f

• Label: 742.2.f
• Level: $742$
• Weight: $2$
• Character orbit: 742.f
• Rep. character: $\chi_{742}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 742 = 2 \cdot 7 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	742.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 371 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(742, [\chi])\).

	Total	New	Old
Modular forms	224	72	152
Cusp forms	208	72	136
Eisenstein series	16	0	16

Trace form

72 * q + 8 * q^14 + 16 * q^15 - 72 * q^16 + 16 * q^18 - 4 * q^21 - 16 * q^22 - 8 * q^23 + 36 * q^35 + 72 * q^36 - 16 * q^39 + 32 * q^42 + 16 * q^44 - 8 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^53 + 8 * q^56 + 24 * q^58 - 16 * q^63 - 16 * q^65 - 8 * q^67 - 32 * q^71 + 16 * q^72 - 8 * q^74 - 48 * q^77 + 40 * q^79 - 104 * q^81 - 4 * q^84 + 16 * q^85 + 8 * q^86 - 16 * q^88 - 8 * q^92 + 48 * q^95 - 16 * q^98 + 80 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(742, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
742.2.f.a	$742$	$2$	742.f	371.g	$4$	$72$	$36$	$5.925$		None		✓	✓	✓	742.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(742, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(742, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(371, [\chi])\)\(^{\oplus 2}\)