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

• Label: 121.2.g
• Level: $121$
• Weight: $2$
• Character orbit: 121.g
• Rep. character: $\chi_{121}(4,\cdot)$
• Character field: $\Q(\zeta_{55})$
• Dimension: $400$
• Newform subspaces: $1$
• Sturm bound: $22$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.g (of order \(55\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{55})\)
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	480	480	0
Cusp forms	400	400	0
Eisenstein series	80	80	0

Trace form

400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9 - 22 * q^10 - 33 * q^11 + 6 * q^12 - 11 * q^13 - 18 * q^14 + 16 * q^15 - 30 * q^16 - 44 * q^17 + 11 * q^18 - 44 * q^19 - 36 * q^20 - 11 * q^21 - 34 * q^23 + 77 * q^24 - 31 * q^25 - 38 * q^26 + 40 * q^27 - 44 * q^28 - 44 * q^29 - 11 * q^30 - 17 * q^31 - 44 * q^32 - 11 * q^33 - 76 * q^34 - 44 * q^35 + 57 * q^36 - 4 * q^37 + 34 * q^38 - 11 * q^39 + 33 * q^40 - 44 * q^41 + 3 * q^42 - 44 * q^43 - 33 * q^44 - 12 * q^45 - 44 * q^46 - 36 * q^47 + 9 * q^48 + 16 * q^49 + 88 * q^50 + 154 * q^51 + 110 * q^52 + 78 * q^53 + 231 * q^54 + 44 * q^55 - 55 * q^56 + 66 * q^57 + 73 * q^58 - 33 * q^59 + 15 * q^60 - 44 * q^61 + 11 * q^62 + 121 * q^63 + 96 * q^64 - 11 * q^65 - 41 * q^67 - 44 * q^68 + 8 * q^69 + 24 * q^70 + 15 * q^71 + 77 * q^72 - 22 * q^73 - 44 * q^74 + 7 * q^75 + 176 * q^76 + 88 * q^77 - 21 * q^78 + 44 * q^79 + 171 * q^80 + 37 * q^81 + 22 * q^82 - 44 * q^83 - 11 * q^84 + 66 * q^85 - 20 * q^86 - 11 * q^87 + 77 * q^88 + 3 * q^89 + 264 * q^90 + 79 * q^91 + 228 * q^92 + 49 * q^93 + 143 * q^94 + 44 * q^95 + 121 * q^96 + 10 * q^97 + 132 * q^98 + 143 * 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.g.a	$121$	$2$	121.g	121.g	$55$	$400$	$10$	$0.966$		None		✓	✓	✓	121.2.g.a	$2$	$0$	\(-44\)	\(-32\)	\(-43\)	\(-44\)		$\mathrm{SU}(2)[C_{55}]$