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

• Label: 2268.2.l
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.l
• Rep. character: $\chi_{2268}(109,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $14$
• Sturm bound: $864$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(864\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(13\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	936	64	872
Cusp forms	792	64	728
Eisenstein series	144	0	144

Trace form

\( 64 q - 5 q^{7} + O(q^{10}) \)

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.l.a	$2268$	$2$	2268.l	63.g	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3q^{5}+(2+\zeta_{6})q^{7}+3q^{11}+(-2+\cdots)q^{13}+\cdots\)
2268.2.l.b	$2268$	$2$	2268.l	63.g	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{5}+(-3+\zeta_{6})q^{7}+2q^{11}+(3+\cdots)q^{13}+\cdots\)
2268.2.l.c	$2268$	$2$	2268.l	63.g	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(-1-2\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{13}+\cdots\)
2268.2.l.d	$2268$	$2$	2268.l	63.g	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(-2+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{13}+\cdots\)
2268.2.l.e	$2268$	$2$	2268.l	63.g	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(1-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{13}+\zeta_{6}q^{19}+\cdots\)
2268.2.l.f	$2268$	$2$	2268.l	63.g	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(2+\zeta_{6})q^{7}+(7-7\zeta_{6})q^{13}-8\zeta_{6}q^{19}+\cdots\)
2268.2.l.g	$2268$	$2$	2268.l	63.g	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2q^{5}+(-3+\zeta_{6})q^{7}-2q^{11}+(3+\cdots)q^{13}+\cdots\)
2268.2.l.h	$2268$	$2$	2268.l	63.g	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3q^{5}+(2+\zeta_{6})q^{7}-3q^{11}+(-2+\cdots)q^{13}+\cdots\)
2268.2.l.i	$2268$	$2$	2268.l	63.g	$3$	$4$	$2$	$18.110$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{5}+(3+2\beta _{2})q^{7}+2\beta _{3}q^{11}+\cdots\)
2268.2.l.j	$2268$	$2$	2268.l	63.g	$3$	$6$	$3$	$18.110$	6.0.309123.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
2268.2.l.k	$2268$	$2$	2268.l	63.g	$3$	$6$	$3$	$18.110$	6.0.309123.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}+\beta _{3})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
2268.2.l.l	$2268$	$2$	2268.l	63.g	$3$	$8$	$4$	$18.110$	8.0.310217769.2	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{6})q^{5}+(\beta _{3}+\beta _{4})q^{7}+(1+\beta _{3}+\cdots)q^{11}+\cdots\)
2268.2.l.m	$2268$	$2$	2268.l	63.g	$3$	$8$	$4$	$18.110$	8.0.310217769.2	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{6})q^{5}+\beta _{7}q^{7}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots\)
2268.2.l.n	$2268$	$2$	2268.l	63.g	$3$	$16$	$8$	$18.110$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{15}q^{5}+(-1+\beta _{1}-\beta _{4})q^{7}-\beta _{11}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 2}\)