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

• Label: 740.2.cf
• Level: $740$
• Weight: $2$
• Character orbit: 740.cf
• Rep. character: $\chi_{740}(7,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $1320$
• 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.cf (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 740 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(228\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	1416	1416	0
Cusp forms	1320	1320	0
Eisenstein series	96	96	0

Trace form

1320 * q - 12 * q^2 - 24 * q^5 - 48 * q^6 - 6 * q^8 - 6 * q^10 - 12 * q^12 - 24 * q^13 - 24 * q^16 - 54 * q^17 + 66 * q^18 - 12 * q^20 - 48 * q^21 - 24 * q^22 - 54 * q^25 - 12 * q^26 - 12 * q^28 - 72 * q^30 - 12 * q^32 - 60 * q^33 - 48 * q^36 - 24 * q^37 + 60 * q^38 + 48 * q^40 - 48 * q^41 + 78 * q^42 - 12 * q^45 - 24 * q^46 + 42 * q^48 - 12 * q^50 + 48 * q^52 - 96 * q^53 - 192 * q^56 - 24 * q^57 + 132 * q^58 - 6 * q^60 - 48 * q^61 + 12 * q^62 - 84 * q^65 + 72 * q^66 - 24 * q^68 + 18 * q^70 - 60 * q^72 + 108 * q^73 - 192 * q^76 - 108 * q^77 - 174 * q^78 - 24 * q^80 - 48 * q^81 - 6 * q^82 + 18 * q^85 - 168 * q^86 - 102 * q^88 - 108 * q^90 - 102 * q^92 + 72 * q^93 - 60 * q^96 - 12 * q^97 - 36 * 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.cf.a	$740$	$2$	740.cf	740.bf	$36$	$12$	$1$	$5.909$	\(\Q(\zeta_{36})\)	\(\Q(\sqrt{-1}) \)		✓			740.2.cf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{36}]$	\(q+(\zeta_{36}^{2}+\zeta_{36}^{11})q^{2}+(-2\zeta_{36}+2\zeta_{36}^{7}+\cdots)q^{4}+\cdots\)
740.2.cf.b	$740$	$2$	740.cf	740.bf	$36$	$12$	$1$	$5.909$	\(\Q(\zeta_{36})\)	\(\Q(\sqrt{-1}) \)		✓			740.2.cf.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{U}(1)[D_{36}]$	\(q+(\zeta_{36}^{2}+\zeta_{36}^{11})q^{2}+(-2\zeta_{36}+2\zeta_{36}^{7}+\cdots)q^{4}+\cdots\)
740.2.cf.c	$740$	$2$	740.cf	740.bf	$36$	$1296$	$108$	$5.909$		None		✓	✓		740.2.cf.c	$8$	$0$	\(-12\)	\(0\)	\(-36\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$