Space of modular forms of level 121, weight 4, and Character 121.g

• Label: 121.4.g
• Level: $121$
• Weight: $4$
• Character orbit: 121.g
• Rep. character: $\chi_{121}(4,\cdot)$
• Character field: $\Q(\zeta_{55})$
• Dimension: $1280$
• Newform subspaces: $1$
• Sturm bound: $44$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(44\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(121, [\chi])\).

	Total	New	Old
Modular forms	1360	1360	0
Cusp forms	1280	1280	0
Eisenstein series	80	80	0

Trace form

1280 * q - 37 * q^2 - 32 * q^3 + 73 * q^4 - 33 * q^5 + 73 * q^6 - 9 * q^7 - 91 * q^8 - 2748 * q^9 + 48 * q^10 + 43 * q^11 + 323 * q^12 - 287 * q^13 - 120 * q^14 + 632 * q^15 + 785 * q^16 - 13 * q^17 + 443 * q^18 - 192 * q^19 - 302 * q^20 - 81 * q^21 - 1483 * q^22 + 790 * q^23 - 1324 * q^24 + 835 * q^25 + 168 * q^26 + 583 * q^27 - 2 * q^28 + 155 * q^29 + 367 * q^30 - 351 * q^31 - 368 * q^32 + 485 * q^33 - 18 * q^34 - 281 * q^35 + 1823 * q^36 - 1097 * q^37 - 362 * q^38 - 112 * q^39 - 3205 * q^40 - 13 * q^41 - 111 * q^42 + 606 * q^43 + 2539 * q^44 + 1888 * q^45 - 1248 * q^46 - 499 * q^47 - 701 * q^48 - 2081 * q^49 + 3931 * q^50 - 1976 * q^51 + 2724 * q^52 + 1993 * q^53 - 2345 * q^54 - 1893 * q^55 - 167 * q^56 + 3462 * q^57 + 1949 * q^58 - 918 * q^59 - 843 * q^60 + 481 * q^61 + 745 * q^62 + 7284 * q^63 - 5887 * q^64 - 2362 * q^65 + 1329 * q^66 - 264 * q^67 - 754 * q^68 + 565 * q^69 + 5580 * q^70 - 27 * q^71 + 4966 * q^72 + 4223 * q^73 + 1432 * q^74 + 789 * q^75 + 6941 * q^76 - 3441 * q^77 - 7413 * q^78 + 5525 * q^79 + 2135 * q^80 - 18615 * q^81 + 3827 * q^82 - 96 * q^83 + 337 * q^84 - 6563 * q^85 - 963 * q^86 - 2057 * q^87 - 1771 * q^88 + 4114 * q^89 + 15586 * q^90 - 3505 * q^91 - 6694 * q^92 + 9192 * q^93 - 14111 * q^94 - 6295 * q^95 - 8919 * q^96 + 1042 * q^97 - 3048 * q^98 + 13103 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(121, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
121.4.g.a	$121$	$4$	121.g	121.g	$55$	$1280$	$32$	$7.139$		None		✓	✓	✓	121.4.g.a	$2$	$0$	\(-37\)	\(-32\)	\(-33\)	\(-9\)		$\mathrm{SU}(2)[C_{55}]$