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

• Label: 740.2.n
• Level: $740$
• Weight: $2$
• Character orbit: 740.n
• Rep. character: $\chi_{740}(223,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $216$
• 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.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
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	236	216	20
Cusp forms	220	216	4
Eisenstein series	16	0	16

Trace form

216 * q - 8 * q^6 - 12 * q^8 - 16 * q^10 - 16 * q^12 + 8 * q^16 + 20 * q^20 - 16 * q^21 + 4 * q^22 + 16 * q^26 - 4 * q^28 - 24 * q^30 - 20 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 36 * q^40 - 40 * q^42 + 40 * q^46 - 36 * q^48 + 24 * q^50 - 20 * q^52 - 16 * q^56 - 32 * q^57 - 16 * q^58 + 20 * q^60 - 64 * q^61 + 4 * q^62 - 32 * q^65 + 52 * q^68 - 24 * q^70 + 40 * q^72 - 16 * q^73 - 24 * q^76 + 48 * q^77 + 24 * q^78 - 56 * q^80 - 136 * q^81 - 4 * q^82 + 48 * q^85 - 88 * q^86 - 64 * q^88 + 120 * q^90 + 56 * q^92 + 16 * q^96 - 80 * q^97 - 64 * 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.n.a	$740$	$2$	740.n	20.e	$4$	$216$	$108$	$5.909$		None		✓	✓	✓	740.2.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(740, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)