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

• Label: 121.4.e
• Level: $121$
• Weight: $4$
• Character orbit: 121.e
• Rep. character: $\chi_{121}(12,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $320$
• Newform subspaces: $1$
• Sturm bound: $44$
• Trace bound: $0$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	340	340	0
Cusp forms	320	320	0
Eisenstein series	20	20	0

Trace form

320 * q - 13 * q^2 - 18 * q^3 - 123 * q^4 - 17 * q^5 - 73 * q^6 - 31 * q^7 + q^8 + 2618 * q^9 - 193 * q^10 - 143 * q^11 - 368 * q^12 + 217 * q^13 + 265 * q^14 - 372 * q^15 - 455 * q^16 + 113 * q^17 - 488 * q^18 - 83 * q^19 - 183 * q^20 - 384 * q^21 + 803 * q^22 - 835 * q^23 + 1464 * q^24 - 825 * q^25 - 43 * q^26 - 528 * q^27 + 117 * q^28 - 155 * q^29 - 42 * q^30 + 691 * q^31 + 93 * q^32 - 330 * q^33 - 27 * q^34 + 161 * q^35 - 1918 * q^36 + 907 * q^37 - 73 * q^38 - 708 * q^39 + 3110 * q^40 - 547 * q^41 + 26 * q^42 + 49 * q^43 - 1474 * q^44 - 1933 * q^45 + 303 * q^46 - 141 * q^47 - 774 * q^48 + 1041 * q^49 - 4071 * q^50 + 2331 * q^51 - 1629 * q^52 - 63 * q^53 + 5500 * q^54 + 3443 * q^55 + 122 * q^56 - 2107 * q^57 - 3204 * q^58 - 447 * q^59 - 912 * q^60 - 851 * q^61 - 3390 * q^62 - 7519 * q^63 + 5137 * q^64 + 1397 * q^65 - 2684 * q^66 + 219 * q^67 - 651 * q^68 - 1540 * q^69 - 5775 * q^70 - 493 * q^71 - 5196 * q^72 - 1723 * q^73 - 17 * q^74 - 164 * q^75 - 7186 * q^76 + 5621 * q^77 + 7368 * q^78 - 5035 * q^79 + 1270 * q^80 + 19880 * q^81 - 897 * q^82 - 479 * q^83 + 428 * q^84 + 3673 * q^85 + 3 * q^86 - 1508 * q^87 - 2959 * q^88 - 4159 * q^89 - 15491 * q^90 + 2035 * q^91 + 9129 * q^92 - 6532 * q^93 + 14346 * q^94 + 4605 * q^95 + 8564 * q^96 - 1947 * q^97 + 1123 * q^98 - 14773 * 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.e.a	$121$	$4$	121.e	121.e	$11$	$320$	$32$	$7.139$		None		✓	✓	✓	121.4.e.a	$2$	$0$	\(-13\)	\(-18\)	\(-17\)	\(-31\)		$\mathrm{SU}(2)[C_{11}]$