Space of modular forms of level 242, weight 2, and Character 242.g

• Label: 242.2.g
• Level: $242$
• Weight: $2$
• Character orbit: 242.g
• Rep. character: $\chi_{242}(5,\cdot)$
• Character field: $\Q(\zeta_{55})$
• Dimension: $440$
• Newform subspaces: $2$
• Sturm bound: $66$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.g (of order \(55\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{55})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(66\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(242, [\chi])\).

	Total	New	Old
Modular forms	1400	440	960
Cusp forms	1240	440	800
Eisenstein series	160	0	160

Trace form

440 * q + q^2 + 2 * q^3 + 11 * q^4 + 4 * q^5 - q^6 - 2 * q^7 + q^8 - 120 * q^9 - 26 * q^10 - 21 * q^11 - 9 * q^12 - 62 * q^13 - 24 * q^14 - 54 * q^15 + 11 * q^16 - 2 * q^17 + 8 * q^18 + 5 * q^19 + 4 * q^20 + 12 * q^21 - 33 * q^22 + 20 * q^23 - q^24 - 5 * q^25 - 8 * q^26 - 13 * q^27 - 2 * q^28 - 10 * q^29 - 6 * q^30 - 50 * q^31 - 4 * q^32 - 11 * q^33 + 14 * q^34 - 12 * q^35 + 16 * q^36 - 58 * q^37 - 78 * q^38 + 6 * q^39 - 26 * q^40 + 2 * q^41 - 2 * q^42 - 6 * q^43 - 4 * q^44 + 68 * q^45 + 4 * q^46 + 2 * q^48 - 89 * q^49 + 11 * q^50 - 114 * q^51 - 6 * q^52 - 68 * q^53 - 48 * q^55 + 8 * q^56 - 16 * q^57 - 60 * q^58 - 11 * q^59 - 8 * q^61 + 2 * q^62 - 126 * q^63 + 11 * q^64 - 82 * q^65 - 27 * q^66 - 60 * q^67 - 2 * q^68 - 30 * q^69 - 44 * q^70 - 64 * q^71 - 7 * q^72 - 30 * q^73 + 18 * q^74 - 13 * q^75 - 45 * q^76 - 36 * q^77 + 48 * q^78 - 80 * q^79 - 6 * q^80 - 149 * q^81 - 49 * q^82 + 19 * q^83 - 8 * q^84 - 222 * q^85 - 31 * q^86 + 20 * q^87 - 32 * q^88 - 80 * q^89 - 188 * q^90 - 210 * q^91 - 98 * q^92 - 96 * q^93 - 188 * q^94 - 166 * q^95 + 4 * q^96 - 91 * q^97 - 76 * q^98 - 97 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(242, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
242.2.g.a	$242$	$2$	242.g	121.g	$55$	$200$	$5$	$1.932$		None		✓			242.2.g.a	$2$	$0$	\(-5\)	\(10\)	\(-1\)	\(0\)		$\mathrm{SU}(2)[C_{55}]$
242.2.g.b	$242$	$2$	242.g	121.g	$55$	$240$	$6$	$1.932$		None		✓	✓		242.2.g.b	$2$	$0$	\(6\)	\(-8\)	\(5\)	\(-2\)		$\mathrm{SU}(2)[C_{55}]$

Decomposition of \(S_{2}^{\mathrm{old}}(242, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(242, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)