Space of modular forms of level 741, weight 2, and Character 741.d

• Label: 741.2.d
• Level: $741$
• Weight: $2$
• Character orbit: 741.d
• Rep. character: $\chi_{741}(740,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $1$
• Sturm bound: $186$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 741 = 3 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	741.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 741 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(186\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(741, [\chi])\).

	Total	New	Old
Modular forms	96	96	0
Cusp forms	88	88	0
Eisenstein series	8	8	0

Trace form

\( 88 q - 88 q^{4} - 4 q^{9} + 72 q^{16} + 64 q^{25} - 60 q^{30} - 48 q^{36} + 20 q^{39} + 48 q^{42} - 64 q^{43} - 112 q^{49} - 24 q^{55} - 64 q^{61} - 104 q^{64} + 12 q^{66} + 60 q^{81} + 56 q^{82} - 32 q^{87}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(741, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
741.2.d.a	$741$	$2$	741.d	741.d	$2$	$88$	$88$	$5.917$		None		✓	✓	✓	741.2.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$