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

• Label: 231.2.l
• Level: $231$
• Weight: $2$
• Character orbit: 231.l
• Rep. character: $\chi_{231}(32,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 231 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	72	72	0
Cusp forms	56	56	0
Eisenstein series	16	16	0

Trace form

56 * q - 2 * q^3 - 28 * q^4 - 6 * q^9 + 6 * q^12 - 12 * q^15 - 44 * q^16 - 24 * q^22 - 12 * q^25 + 4 * q^27 - 22 * q^33 + 56 * q^34 + 28 * q^36 + 96 * q^42 + 14 * q^45 - 104 * q^48 - 4 * q^49 - 88 * q^55 + 16 * q^58 - 48 * q^60 + 192 * q^64 - 42 * q^66 + 20 * q^67 - 28 * q^69 - 76 * q^70 + 46 * q^75 + 104 * q^78 + 2 * q^81 - 4 * q^82 - 16 * q^88 + 48 * q^91 + 48 * q^93 - 80 * q^97 - 20 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
231.2.l.a	$231$	$2$	231.l	231.l	$6$	$8$	$4$	$1.845$	8.0.\(\cdots\).5	None		✓			231.2.l.a	$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{4})q^{3}+2\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots\)
231.2.l.b	$231$	$2$	231.l	231.l	$6$	$48$	$24$	$1.845$		None		✓	✓		231.2.l.b	$8$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$