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

• Label: 2268.2.x
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.x
• Rep. character: $\chi_{2268}(377,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $11$
• Sturm bound: $864$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.x (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(864\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

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

\( 64 q + 5 q^{7} - 32 q^{25} - 20 q^{37} - 20 q^{43} + 7 q^{49} + 2 q^{67} - 82 q^{79} - 12 q^{85} + 18 q^{91}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2268.2.x.a	$2268$	$2$	2268.x	63.o	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None					756.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(-3-3\zeta_{6})q^{11}+\cdots\)
2268.2.x.b	$2268$	$2$	2268.x	63.o	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None					756.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(3+3\zeta_{6})q^{11}+\cdots\)
2268.2.x.c	$2268$	$2$	2268.x	63.o	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					84.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-3+\zeta_{6})q^{7}+(-8+4\zeta_{6})q^{13}+\cdots\)
2268.2.x.d	$2268$	$2$	2268.x	63.o	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					756.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2-3\zeta_{6})q^{7}+(2-\zeta_{6})q^{13}+(-5+\cdots)q^{19}+\cdots\)
2268.2.x.e	$2268$	$2$	2268.x	63.o	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					84.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1+3\zeta_{6})q^{7}+(8-4\zeta_{6})q^{13}+(-2+\cdots)q^{19}+\cdots\)
2268.2.x.f	$2268$	$2$	2268.x	63.o	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					756.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(3-2\zeta_{6})q^{7}+(-2+\zeta_{6})q^{13}+(5+\cdots)q^{19}+\cdots\)
2268.2.x.g	$2268$	$2$	2268.x	63.o	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None					756.2.f.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(3+3\zeta_{6})q^{11}+\cdots\)
2268.2.x.h	$2268$	$2$	2268.x	63.o	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None					756.2.f.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-3-3\zeta_{6})q^{11}+\cdots\)
2268.2.x.i	$2268$	$2$	2268.x	63.o	$6$	$8$	$4$	$18.110$	\(\Q(\zeta_{24})\)	None					252.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_{2} q^{5}+(\beta_{5}-\beta_1+1)q^{7}+(-\beta_{7}-\beta_{3})q^{11}+\cdots\)
2268.2.x.j	$2268$	$2$	2268.x	63.o	$6$	$8$	$4$	$18.110$	\(\Q(\zeta_{24})\)	None					756.2.f.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{4}-\beta_{2})q^{5}+(-\beta_{6}+\beta_1)q^{7}+\cdots\)
2268.2.x.k	$2268$	$2$	2268.x	63.o	$6$	$32$	$16$	$18.110$		None		✓	✓		2268.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 2}\)