Space of modular forms of level 121, weight 2, and Character 121.e

• Label: 121.2.e
• Level: $121$
• Weight: $2$
• Character orbit: 121.e
• Rep. character: $\chi_{121}(12,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $100$
• Newform subspaces: $1$
• Sturm bound: $22$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.e (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(22\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(121, [\chi])\).

	Total	New	Old
Modular forms	120	120	0
Cusp forms	100	100	0
Eisenstein series	20	20	0

Trace form

100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9 - 13 * q^10 - 12 * q^11 - 51 * q^12 - 34 * q^13 - 17 * q^14 - 46 * q^15 + 10 * q^16 + 9 * q^17 - 31 * q^18 + 9 * q^19 + 21 * q^20 - 14 * q^21 - 20 * q^22 - 11 * q^23 - 72 * q^24 + 11 * q^25 + 33 * q^26 - 60 * q^27 + 49 * q^28 + 19 * q^29 + 26 * q^30 - 13 * q^31 + 44 * q^32 + q^33 + 31 * q^34 + 39 * q^35 - 17 * q^36 - 16 * q^37 - 29 * q^38 + 16 * q^39 + 2 * q^40 + 39 * q^41 + 42 * q^42 + 39 * q^43 + 53 * q^44 - 33 * q^45 + 59 * q^46 + 21 * q^47 + 56 * q^48 - 11 * q^49 - 58 * q^50 - 139 * q^51 - 75 * q^52 - 73 * q^53 - 156 * q^54 - 34 * q^55 + 10 * q^56 - 41 * q^57 - 38 * q^58 + 33 * q^59 + 100 * q^60 + 39 * q^61 + 44 * q^62 - 76 * q^63 - 16 * q^64 + 36 * q^65 + 75 * q^66 - 4 * q^67 + 119 * q^68 + 32 * q^69 + 61 * q^70 + 5 * q^71 + 63 * q^72 + 37 * q^73 + 109 * q^74 + 58 * q^75 - 91 * q^76 - 53 * q^77 - 24 * q^78 - 9 * q^79 - 36 * q^80 + 28 * q^81 + 33 * q^82 + 79 * q^83 + 176 * q^84 - 11 * q^85 + 85 * q^86 + 76 * q^87 + 33 * q^88 - 48 * q^89 - 89 * q^90 - 14 * q^91 - 113 * q^92 + 31 * q^93 - 38 * q^94 + 21 * q^95 + 84 * q^96 + 40 * q^97 - 22 * q^98 - 53 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(121, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
121.2.e.a	$121$	$2$	121.e	121.e	$11$	$100$	$10$	$0.966$		None		✓	✓	✓	121.2.e.a	$2$	$0$	\(-6\)	\(-18\)	\(-7\)	\(-1\)		$\mathrm{SU}(2)[C_{11}]$