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

• Label: 2268.2.k
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.k
• Rep. character: $\chi_{2268}(1297,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $7$
• Sturm bound: $864$
• Trace bound: $5$

Defining parameters

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

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

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

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.k.a	$2268$	$2$	2268.k	7.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
2268.2.k.b	$2268$	$2$	2268.k	7.c	$3$	$2$	$1$	$18.110$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2268.2.k.c	$2268$	$2$	2268.k	7.c	$3$	$8$	$4$	$18.110$	8.0.310217769.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{5}-\beta _{4}q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2268.2.k.d	$2268$	$2$	2268.k	7.c	$3$	$8$	$4$	$18.110$	8.0.310217769.2	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(1\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{5}-\beta _{4}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2268.2.k.e	$2268$	$2$	2268.k	7.c	$3$	$14$	$7$	$18.110$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-3\)	$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{5}-\beta _{10}q^{7}-\beta _{13}q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)
2268.2.k.f	$2268$	$2$	2268.k	7.c	$3$	$14$	$7$	$18.110$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-3\)	$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{5}-\beta _{10}q^{7}+\beta _{13}q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)
2268.2.k.g	$2268$	$2$	2268.k	7.c	$3$	$16$	$8$	$18.110$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{13}q^{5}-\beta _{7}q^{7}-\beta _{12}q^{11}+(-3+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 2}\)