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

• Label: 242.2.e
• Level: $242$
• Weight: $2$
• Character orbit: 242.e
• Rep. character: $\chi_{242}(23,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $110$
• 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.e (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{11})\)
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	350	110	240
Cusp forms	310	110	200
Eisenstein series	40	0	40

Trace form

110 * q - q^2 - 2 * q^3 - 11 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 - q^8 + 100 * q^9 + 16 * q^10 + 11 * q^11 + 9 * q^12 + 52 * q^13 + 14 * q^14 + 24 * q^15 - 11 * q^16 - 18 * q^17 - 13 * q^18 - 20 * q^19 - 4 * q^20 - 32 * q^21 + 33 * q^22 - 20 * q^23 - 4 * q^24 - 35 * q^25 - 12 * q^26 - 32 * q^27 - 8 * q^28 - 30 * q^29 - 24 * q^30 + 20 * q^31 - q^32 - 44 * q^33 - 14 * q^34 - 48 * q^35 - 21 * q^36 + 38 * q^37 + 48 * q^38 - 56 * q^39 + 16 * q^40 - 42 * q^41 - 28 * q^42 - 44 * q^43 - 11 * q^44 - 68 * q^45 - 24 * q^46 - 40 * q^47 - 2 * q^48 + 29 * q^49 - 31 * q^50 + 49 * q^51 - 14 * q^52 + 18 * q^53 - 40 * q^54 - 22 * q^55 - 8 * q^56 - 69 * q^57 + 20 * q^58 - 54 * q^59 - 20 * q^60 - 62 * q^61 - 32 * q^62 + 6 * q^63 - 11 * q^64 - 18 * q^65 - 33 * q^66 + 60 * q^67 - 18 * q^68 - 80 * q^69 + 4 * q^70 - 16 * q^71 - 13 * q^72 - 30 * q^73 - 38 * q^74 - 102 * q^75 + 35 * q^76 - 44 * q^77 - 48 * q^78 + 30 * q^79 - 4 * q^80 + 14 * q^81 + 14 * q^82 - 84 * q^83 - 32 * q^84 + 112 * q^85 - 34 * q^86 - 120 * q^87 + 22 * q^88 + 80 * q^89 + 98 * q^90 + 110 * q^91 + 68 * q^92 - 34 * q^93 + 128 * q^94 + 56 * q^95 - 4 * q^96 - 4 * q^97 + 31 * q^98 - 33 * 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.e.a	$242$	$2$	242.e	121.e	$11$	$50$	$5$	$1.932$		None		✓			242.2.e.a	$2$	$0$	\(5\)	\(-10\)	\(1\)	\(0\)		$\mathrm{SU}(2)[C_{11}]$
242.2.e.b	$242$	$2$	242.e	121.e	$11$	$60$	$6$	$1.932$		None		✓	✓		242.2.e.b	$2$	$0$	\(-6\)	\(8\)	\(-5\)	\(-8\)		$\mathrm{SU}(2)[C_{11}]$

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

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