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

• Label: 1140.2.bg
• Level: $1140$
• Weight: $2$
• Character orbit: 1140.bg
• Rep. character: $\chi_{1140}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.bg (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	504	40	464
Cusp forms	456	40	416
Eisenstein series	48	0	48

Trace form

40 * q - 2 * q^5 + 20 * q^9 - 2 * q^15 - 16 * q^19 - 4 * q^21 - 12 * q^25 + 8 * q^29 - 8 * q^31 - 2 * q^35 + 8 * q^39 - 4 * q^41 - 4 * q^45 - 32 * q^49 - 8 * q^51 + 12 * q^55 - 48 * q^59 + 4 * q^65 - 40 * q^69 + 16 * q^71 - 8 * q^75 + 24 * q^79 - 20 * q^81 + 48 * q^85 + 32 * q^89 + 4 * q^91 + 26 * q^95

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.bg.a	$1140$	$2$	1140.bg	95.i	$6$	$4$	$2$	$9.103$	\(\Q(\zeta_{12})\)	None		✓			1140.2.bg.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1140.2.bg.b	$1140$	$2$	1140.bg	95.i	$6$	$4$	$2$	$9.103$	\(\Q(\zeta_{12})\)	None		✓			1140.2.bg.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1140.2.bg.c	$1140$	$2$	1140.bg	95.i	$6$	$32$	$16$	$9.103$		None		✓	✓		1140.2.bg.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)