Space of modular forms of level 2268, weight 2, and Character 2268.j

• Label: 2268.2.j
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.j
• Rep. character: $\chi_{2268}(757,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $18$
• Sturm bound: $864$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(864\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2268, [\chi])\).

	Total	New	Old
Modular forms	936	48	888
Cusp forms	792	48	744
Eisenstein series	144	0	144

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2268, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2268.2.j.a	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2268.2.j.b	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2268.2.j.c	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
2268.2.j.d	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2268.2.j.e	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2268.2.j.f	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2268.2.j.g	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2268.2.j.h	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+4\zeta_{6}q^{13}+\cdots\)
2268.2.j.i	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}-2\zeta_{6}q^{13}+\cdots\)
2268.2.j.j	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2268.2.j.k	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
2268.2.j.l	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
2268.2.j.m	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2268.2.j.n	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2268.2.j.o	$2268$	$2$	2268.j	9.c	$3$	$4$	$2$	$18.110$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}^{2}q^{5}+(-1+\zeta_{12})q^{7}+(2\zeta_{12}^{2}+\cdots)q^{11}+\cdots\)
2268.2.j.p	$2268$	$2$	2268.j	9.c	$3$	$4$	$2$	$18.110$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{12}^{2}q^{5}+(-1+\zeta_{12})q^{7}+(\zeta_{12}^{2}+\cdots)q^{11}+\cdots\)
2268.2.j.q	$2268$	$2$	2268.j	9.c	$3$	$4$	$2$	$18.110$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{5}+(1-\beta _{1})q^{7}+(-\beta _{2}-\beta _{3})q^{11}+\cdots\)
2268.2.j.r	$2268$	$2$	2268.j	9.c	$3$	$8$	$4$	$18.110$	8.0.2702336256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}-\beta _{6})q^{5}+(1-\beta _{2})q^{7}+(\beta _{4}+\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 2}\)