Space of modular forms of level 468, weight 2, and Character 468.s

• Label: 468.2.s
• Level: $468$
• Weight: $2$
• Character orbit: 468.s
• Rep. character: $\chi_{468}(35,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $168$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 156 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(168\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(468, [\chi])\).

	Total	New	Old
Modular forms	184	56	128
Cusp forms	152	56	96
Eisenstein series	32	0	32

Trace form

\( 56 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(468, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
468.2.s.a	$468$	$2$	468.s	156.p	$6$	$4$	$2$	$3.737$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}-2q^{4}-\beta _{3}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
468.2.s.b	$468$	$2$	468.s	156.p	$6$	$4$	$2$	$3.737$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{3}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
468.2.s.c	$468$	$2$	468.s	156.p	$6$	$8$	$4$	$3.737$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{U}(1)[D_{6}]$	\(q+\zeta_{24}^{5}q^{2}+(2-2\zeta_{24}^{2})q^{4}+(2\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
468.2.s.d	$468$	$2$	468.s	156.p	$6$	$40$	$20$	$3.737$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(468, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(468, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)