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

• Label: 1134.2.h
• Level: $1134$
• Weight: $2$
• Character orbit: 1134.h
• Rep. character: $\chi_{1134}(109,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $22$
• Sturm bound: $432$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(432\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	480	64	416
Cusp forms	384	64	320
Eisenstein series	96	0	96

Trace form

\( 64 q - 32 q^{4} + 10 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1134.2.h.a	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+(-1+\cdots)q^{7}+\cdots\)
1134.2.h.b	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2q^{5}+(-3+\cdots)q^{7}+\cdots\)
1134.2.h.c	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
1134.2.h.d	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.h.e	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1134.2.h.f	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+(-3+\cdots)q^{7}+\cdots\)
1134.2.h.g	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(6\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+(2+\cdots)q^{7}+\cdots\)
1134.2.h.h	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4q^{5}+(3+\cdots)q^{7}+\cdots\)
1134.2.h.i	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1134.2.h.j	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+(-3+\cdots)q^{7}+\cdots\)
1134.2.h.k	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-6\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.h.l	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1134.2.h.m	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
1134.2.h.n	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.h.o	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}+(-3+\cdots)q^{7}+\cdots\)
1134.2.h.p	$1134$	$2$	1134.h	63.g	$3$	$2$	$1$	$9.055$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+(-1+\cdots)q^{7}+\cdots\)
1134.2.h.q	$1134$	$2$	1134.h	63.g	$3$	$4$	$2$	$9.055$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
1134.2.h.r	$1134$	$2$	1134.h	63.g	$3$	$4$	$2$	$9.055$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{4}+(1+\beta _{2})q^{7}+\cdots\)
1134.2.h.s	$1134$	$2$	1134.h	63.g	$3$	$4$	$2$	$9.055$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1})q^{2}+\beta _{1}q^{4}+(1-\beta _{2})q^{7}+\cdots\)
1134.2.h.t	$1134$	$2$	1134.h	63.g	$3$	$4$	$2$	$9.055$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
1134.2.h.u	$1134$	$2$	1134.h	63.g	$3$	$8$	$4$	$9.055$	8.0.454201344.7	None		$2$	$0$	\(-4\)	\(0\)	\(-8\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(-1-\beta _{4})q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
1134.2.h.v	$1134$	$2$	1134.h	63.g	$3$	$8$	$4$	$9.055$	8.0.454201344.7	None		$2$	$0$	\(4\)	\(0\)	\(8\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(-1-\beta _{4})q^{4}+(1+\beta _{5})q^{5}+\cdots\)

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

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