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

• Label: 740.2.bg
• Level: $740$
• Weight: $2$
• Character orbit: 740.bg
• Rep. character: $\chi_{740}(47,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $440$
• Newform subspaces: $3$
• Sturm bound: $228$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.bg (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 740 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(228\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	472	472	0
Cusp forms	440	440	0
Eisenstein series	32	32	0

Trace form

440 * q - 2 * q^2 - 4 * q^5 - 16 * q^6 - 8 * q^8 - 8 * q^10 + 10 * q^12 - 8 * q^13 - 4 * q^16 + 6 * q^17 - 18 * q^18 - 18 * q^20 - 8 * q^21 + 2 * q^22 + 6 * q^25 - 48 * q^26 - 2 * q^28 - 12 * q^30 - 2 * q^32 + 8 * q^33 - 80 * q^36 + 2 * q^37 - 84 * q^38 - 22 * q^40 + 8 * q^41 + 52 * q^42 - 36 * q^45 - 52 * q^46 - 24 * q^48 - 2 * q^50 - 38 * q^52 + 24 * q^53 - 80 * q^56 + 20 * q^57 - 24 * q^58 - 32 * q^60 - 8 * q^61 + 2 * q^62 - 14 * q^65 - 144 * q^66 - 40 * q^68 - 12 * q^70 + 26 * q^72 - 120 * q^73 + 36 * q^76 + 24 * q^77 + 24 * q^78 + 12 * q^80 + 148 * q^81 - 40 * q^82 + 24 * q^85 + 4 * q^86 + 148 * q^88 + 66 * q^90 + 28 * q^92 + 8 * q^96 + 4 * q^97 + 54 * q^98

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.bg.a	$740$	$2$	740.bg	740.ag	$12$	$4$	$1$	$5.909$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			740.2.bg.a	$4$	$0$	\(2\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
740.2.bg.b	$740$	$2$	740.bg	740.ag	$12$	$4$	$1$	$5.909$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			740.2.bg.a	$4$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
740.2.bg.c	$740$	$2$	740.bg	740.ag	$12$	$432$	$108$	$5.909$		None		✓	✓		740.2.bg.c	$8$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$