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

• Label: 2268.2.t
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.t
• Rep. character: $\chi_{2268}(1781,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $864$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(864\)
Trace bound:			\(11\)
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.t.a	$2268$	$2$	2268.t	21.g	$6$	$16$	$8$	$18.110$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{5}+\beta _{3}q^{7}+\beta _{15}q^{11}+\beta _{1}q^{13}+\cdots\)
2268.2.t.b	$2268$	$2$	2268.t	21.g	$6$	$16$	$8$	$18.110$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{11}q^{5}-\beta _{4}q^{7}+(-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
2268.2.t.c	$2268$	$2$	2268.t	21.g	$6$	$32$	$16$	$18.110$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{6}]$

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

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