Space of modular forms of level 74, weight 4, and Character 74.b

• Label: 74.4.b
• Level: $74$
• Weight: $4$
• Character orbit: 74.b
• Rep. character: $\chi_{74}(73,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(38\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(74, [\chi])\).

	Total	New	Old
Modular forms	30	10	20
Cusp forms	26	10	16
Eisenstein series	4	0	4

Trace form

\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(74, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
74.4.b.a	$74$	$4$	74.b	37.b	$2$	$10$	$10$	$4.366$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(14\)	\(0\)	\(-4\)	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(1-\beta _{2})q^{3}-4q^{4}+(2\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)