Space of modular forms of level 740, weight 2, and Character 740.br

• Label: 740.2.br
• Level: $740$
• Weight: $2$
• Character orbit: 740.br
• Rep. character: $\chi_{740}(9,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $108$
• Newform subspaces: $1$
• Sturm bound: $228$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.br (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(228\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(740, [\chi])\).

	Total	New	Old
Modular forms	720	108	612
Cusp forms	648	108	540
Eisenstein series	72	0	72

Trace form

108 * q + 6 * q^9 + 12 * q^11 - 9 * q^15 + 6 * q^19 + 12 * q^21 + 30 * q^25 + 60 * q^31 - 24 * q^35 - 48 * q^39 + 36 * q^41 - 57 * q^45 - 30 * q^49 - 15 * q^55 - 30 * q^59 - 12 * q^61 - 33 * q^65 - 12 * q^69 + 66 * q^71 - 12 * q^75 + 12 * q^81 + 6 * q^85 - 36 * q^89 + 6 * q^91 - 105 * q^95 + 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(740, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
740.2.br.a	$740$	$2$	740.br	185.x	$18$	$108$	$18$	$5.909$		None		✓	✓	✓	740.2.br.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(740, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(740, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)