Space of modular forms of level 74, weight 5, and Character 74.i

• Label: 74.5.i
• Level: $74$
• Weight: $5$
• Character orbit: 74.i
• Rep. character: $\chi_{74}(5,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $144$
• Newform subspaces: $2$
• Sturm bound: $47$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.i (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(47\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(74, [\chi])\).

	Total	New	Old
Modular forms	480	144	336
Cusp forms	432	144	288
Eisenstein series	48	0	48

Trace form

\( 144 q + 36 q^{5} - 420 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
74.5.i.a	$74$	$5$	74.i	37.i	$36$	$72$	$6$	$7.649$		None		$2$	$0$	\(0\)	\(0\)	\(-78\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
74.5.i.b	$74$	$5$	74.i	37.i	$36$	$72$	$6$	$7.649$		None		$2$	$0$	\(0\)	\(0\)	\(114\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{5}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)