Space of modular forms of level 1134, weight 2, and Character 1134.f

• Label: 1134.2.f
• Level: $1134$
• Weight: $2$
• Character orbit: 1134.f
• Rep. character: $\chi_{1134}(379,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $20$
• Sturm bound: $432$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(432\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1134, [\chi])\).

	Total	New	Old
Modular forms	480	48	432
Cusp forms	384	48	336
Eisenstein series	96	0	96

Trace form

48 * q - 24 * q^4 - 24 * q^16 - 24 * q^19 + 12 * q^22 + 24 * q^31 + 12 * q^34 - 48 * q^37 + 12 * q^43 - 24 * q^49 - 48 * q^55 + 48 * q^64 + 36 * q^67 - 24 * q^73 + 12 * q^76 + 24 * q^79 + 12 * q^85 + 12 * q^88 - 48 * q^91 + 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1134, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1134.2.f.a	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					378.2.a.a	$2$	$0$	\(-1\)	\(0\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
1134.2.f.b	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					378.2.a.b	$2$	$0$	\(-1\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
1134.2.f.c	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					378.2.a.c	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1134.2.f.d	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		✓			1134.2.a.b	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1134.2.f.e	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					378.2.a.d	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots\)
1134.2.f.f	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					14.2.a.a	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots\)
1134.2.f.g	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					42.2.a.a	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
1134.2.f.h	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		✓			1134.2.a.d	$2$	$0$	\(-1\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
1134.2.f.i	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		✓			1134.2.a.d	$2$	$0$	\(1\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1134.2.f.j	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					42.2.a.a	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1134.2.f.k	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					378.2.a.d	$2$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots\)
1134.2.f.l	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					14.2.a.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots\)
1134.2.f.m	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		✓			1134.2.a.b	$2$	$0$	\(1\)	\(0\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1134.2.f.n	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					378.2.a.c	$2$	$0$	\(1\)	\(0\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1134.2.f.o	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					378.2.a.b	$2$	$0$	\(1\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1134.2.f.p	$1134$	$2$	1134.f	9.c	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None					378.2.a.a	$2$	$0$	\(1\)	\(0\)	\(4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1134.2.f.q	$1134$	$2$	1134.f	9.c	$3$	$4$	$2$	$9.055$	\(\Q(\zeta_{12})\)	None		✓			1134.2.a.j	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_1-1)q^{2}-\beta_1 q^{4}-\beta_{2} q^{5}+\cdots\)
1134.2.f.r	$1134$	$2$	1134.f	9.c	$3$	$4$	$2$	$9.055$	\(\Q(\zeta_{12})\)	None		✓			1134.2.a.l	$2$	$0$	\(-2\)	\(0\)	\(4\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_1 q^{2}+(\beta_1-1)q^{4}+(\beta_{3}-\beta_{2}-2\beta_1+2)q^{5}+\cdots\)
1134.2.f.s	$1134$	$2$	1134.f	9.c	$3$	$4$	$2$	$9.055$	\(\Q(\zeta_{12})\)	None		✓			1134.2.a.l	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_1+1)q^{2}-\beta_1 q^{4}+(\beta_{2}-2\beta_1)q^{5}+\cdots\)
1134.2.f.t	$1134$	$2$	1134.f	9.c	$3$	$4$	$2$	$9.055$	\(\Q(\zeta_{12})\)	None		✓			1134.2.a.j	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_1+1)q^{2}-\beta_1 q^{4}-\beta_{2} q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)