Space of modular forms of level 1140, weight 2, and Character 1140.z

• Label: 1140.2.z
• Level: $1140$
• Weight: $2$
• Character orbit: 1140.z
• Rep. character: $\chi_{1140}(449,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $480$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(480\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

	Total	New	Old
Modular forms	504	80	424
Cusp forms	456	80	376
Eisenstein series	48	0	48

Trace form

\( 80 q + 3 q^{15} - 4 q^{19} + 2 q^{25} + 6 q^{45} - 56 q^{49} + 54 q^{51} - 12 q^{55} + 12 q^{61} + 24 q^{79} - 4 q^{81} + 10 q^{85} + 60 q^{91} + 12 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1140.2.z.a	$1140$	$2$	1140.z	285.q	$6$	$80$	$40$	$9.103$		None		✓	✓	✓	1140.2.z.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)