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

• Label: 2268.2.bm
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.bm
• Rep. character: $\chi_{2268}(593,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $10$
• 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.bm (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(864\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(13\)

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

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

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.bm.a	$2268$	$2$	2268.bm	63.s	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-3q^{5}+(2-3\zeta_{6})q^{7}+(-3+6\zeta_{6})q^{11}+\cdots\)
2268.2.bm.b	$2268$	$2$	2268.bm	63.s	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2-\zeta_{6})q^{7}+(1+\zeta_{6})q^{13}+(4-2\zeta_{6})q^{19}+\cdots\)
2268.2.bm.c	$2268$	$2$	2268.bm	63.s	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2-3\zeta_{6})q^{7}+(-3-3\zeta_{6})q^{13}+(-4+\cdots)q^{19}+\cdots\)
2268.2.bm.d	$2268$	$2$	2268.bm	63.s	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1+3\zeta_{6})q^{7}+(3+3\zeta_{6})q^{13}+(-10+\cdots)q^{19}+\cdots\)
2268.2.bm.e	$2268$	$2$	2268.bm	63.s	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+2\zeta_{6})q^{7}+(4+4\zeta_{6})q^{13}+(10+\cdots)q^{19}+\cdots\)
2268.2.bm.f	$2268$	$2$	2268.bm	63.s	$6$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3q^{5}+(2-3\zeta_{6})q^{7}+(3-6\zeta_{6})q^{11}+\cdots\)
2268.2.bm.g	$2268$	$2$	2268.bm	63.s	$6$	$4$	$2$	$18.110$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{5}+(-2-\beta _{1})q^{7}+(2\beta _{2}-\beta _{3})q^{11}+\cdots\)
2268.2.bm.h	$2268$	$2$	2268.bm	63.s	$6$	$4$	$2$	$18.110$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{5}+(1-2\beta _{2})q^{7}+(-2+2\beta _{2}+\cdots)q^{13}+\cdots\)
2268.2.bm.i	$2268$	$2$	2268.bm	63.s	$6$	$12$	$6$	$18.110$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{9}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{5}-\beta _{3}q^{7}+(-\beta _{1}-\beta _{7})q^{11}+\cdots\)
2268.2.bm.j	$2268$	$2$	2268.bm	63.s	$6$	$32$	$16$	$18.110$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$

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

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