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

• Label: 740.2.e
• Level: $740$
• Weight: $2$
• Character orbit: 740.e
• Rep. character: $\chi_{740}(369,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• 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.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q\)
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	120	20	100
Cusp forms	108	20	88
Eisenstein series	12	0	12

Trace form

\( 20 q - 28 q^{9} - 8 q^{25} - 8 q^{41} - 28 q^{49} - 20 q^{65} + 56 q^{71} - 28 q^{75} + 20 q^{81} - 20 q^{85} - 20 q^{95} + 40 q^{99}+O(q^{100}) \)

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.e.a	$740$	$2$	740.e	185.d	$2$	$20$	$20$	$5.909$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓	✓	740.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+(-1-\beta _{14}+\cdots)q^{9}+\cdots\)

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

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