Space of modular forms of level 231, weight 2, and Character 231.w

• Label: 231.2.w
• Level: $231$
• Weight: $2$
• Character orbit: 231.w
• Rep. character: $\chi_{231}(13,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.w (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(231, [\chi])\).

	Total	New	Old
Modular forms	144	64	80
Cusp forms	112	64	48
Eisenstein series	32	0	32

Trace form

\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
231.2.w.a	$231$	$2$	231.w	77.l	$10$	$64$	$16$	$1.845$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(231, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)