Space of modular forms of level 246, weight 2, and Character 246.o

• Label: 246.2.o
• Level: $246$
• Weight: $2$
• Character orbit: 246.o
• Rep. character: $\chi_{246}(11,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $224$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 246 = 2 \cdot 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	246.o (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 123 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(246, [\chi])\).

	Total	New	Old
Modular forms	736	224	512
Cusp forms	608	224	384
Eisenstein series	128	0	128

Trace form

224 * q - 4 * q^3 - 12 * q^9 + 24 * q^15 + 56 * q^16 - 16 * q^21 + 8 * q^22 + 4 * q^24 + 20 * q^27 - 32 * q^30 - 164 * q^33 - 24 * q^34 - 8 * q^36 + 16 * q^37 - 128 * q^39 - 128 * q^42 - 32 * q^43 - 160 * q^45 - 16 * q^46 - 16 * q^48 - 48 * q^49 - 64 * q^51 - 60 * q^54 + 32 * q^55 + 16 * q^57 - 16 * q^58 + 48 * q^61 - 8 * q^63 - 64 * q^67 - 8 * q^69 - 48 * q^70 - 80 * q^73 - 16 * q^75 + 8 * q^76 - 80 * q^79 + 24 * q^82 + 16 * q^84 - 256 * q^85 + 40 * q^87 + 40 * q^90 - 80 * q^91 - 112 * q^93 + 48 * q^94 - 128 * q^97 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(246, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
246.2.o.a	$246$	$2$	246.o	123.o	$40$	$112$	$7$	$1.964$		None		✓			246.2.o.a	$2$	$0$	\(0\)	\(-4\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{40}]$
246.2.o.b	$246$	$2$	246.o	123.o	$40$	$112$	$7$	$1.964$		None		✓			246.2.o.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{40}]$

Decomposition of \(S_{2}^{\mathrm{old}}(246, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(246, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 2}\)