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

• Label: 121.4.c
• Level: $121$
• Weight: $4$
• Character orbit: 121.c
• Rep. character: $\chi_{121}(3,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $92$
• Newform subspaces: $10$
• Sturm bound: $44$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(44\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	156	124	32
Cusp forms	108	92	16
Eisenstein series	48	32	16

Trace form

92 * q + 7 * q^2 + 5 * q^3 - 83 * q^4 + 3 * q^5 + 29 * q^6 + 35 * q^7 - 47 * q^8 - 182 * q^9 - 40 * q^10 - 358 * q^12 + 65 * q^13 + 248 * q^14 + 83 * q^15 + 245 * q^16 + 31 * q^17 + 102 * q^18 - 148 * q^19 - 426 * q^20 - 334 * q^21 + 52 * q^23 + 447 * q^24 + 148 * q^25 + 148 * q^26 - 166 * q^27 + 42 * q^28 + 199 * q^29 + 114 * q^30 + 369 * q^31 - 324 * q^32 + 530 * q^34 - 237 * q^35 - 26 * q^36 - 33 * q^37 + 290 * q^38 - 365 * q^39 - 532 * q^40 + 31 * q^41 + 294 * q^42 + 650 * q^43 - 1204 * q^45 - 1204 * q^46 - 1259 * q^47 - 254 * q^48 - 1110 * q^49 + 147 * q^50 + 246 * q^51 + 590 * q^52 + 1719 * q^53 + 3100 * q^54 + 2664 * q^56 - 102 * q^57 - 1048 * q^58 - 478 * q^59 - 400 * q^60 + 525 * q^61 - 2456 * q^62 + 68 * q^63 + 861 * q^64 - 1790 * q^65 - 806 * q^67 - 710 * q^68 - 228 * q^69 + 288 * q^70 - 1027 * q^71 - 919 * q^72 + 2155 * q^73 + 1476 * q^74 + 54 * q^75 + 242 * q^76 + 2716 * q^78 + 861 * q^79 + 3156 * q^80 + 1489 * q^81 + 3915 * q^82 - 52 * q^83 + 84 * q^84 - 2383 * q^85 - 1203 * q^86 - 2310 * q^87 - 5382 * q^89 + 1682 * q^90 - 3871 * q^91 + 1158 * q^92 - 2013 * q^93 - 702 * q^94 + 1317 * q^95 - 1252 * q^96 - 2094 * q^97 - 2740 * q^98

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.c.a	$121$	$4$	121.c	11.c	$5$	$4$	$1$	$7.139$	\(\Q(\zeta_{10})\)	\(\Q(\sqrt{-11}) \)		✓			121.4.a.a	$8$	$0$	\(0\)	\(-8\)	\(-18\)	\(0\)	$1$	$\mathrm{U}(1)[D_{5}]$	\(q+8\zeta_{10}^{2}q^{3}+8\zeta_{10}^{3}q^{4}-18\zeta_{10}q^{5}+\cdots\)
121.4.c.b	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.\(\cdots\).1	None					11.4.c.a	$2$	$0$	\(-3\)	\(-3\)	\(18\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
121.4.c.c	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None					11.4.a.a	$4$	$0$	\(-2\)	\(2\)	\(-2\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{2}+\beta _{7})q^{2}+(-4\beta _{1}-\beta _{6})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.d	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None		✓			121.4.a.b	$4$	$0$	\(-2\)	\(8\)	\(10\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{2}-\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.e	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.\(\cdots\).7	None		✓			121.4.a.d	$8$	$0$	\(0\)	\(10\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{2}-5\beta _{6}q^{3}+18\beta _{4}q^{4}+(-5+\cdots)q^{5}+\cdots\)
121.4.c.f	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None					11.4.a.a	$4$	$0$	\(2\)	\(2\)	\(-2\)	\(20\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{2}+\beta _{7})q^{2}+(4\beta _{1}-\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.g	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.324000000.3	None		✓			121.4.a.b	$4$	$0$	\(2\)	\(8\)	\(10\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{2}+\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.h	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.\(\cdots\).1	None					11.4.c.a	$2$	$0$	\(3\)	\(-3\)	\(18\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+2\beta _{4}+\beta _{6}-\beta _{7})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
121.4.c.i	$121$	$4$	121.c	11.c	$5$	$8$	$2$	$7.139$	8.0.\(\cdots\).1	None					11.4.c.a	$2$	$0$	\(7\)	\(-3\)	\(-7\)	\(35\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
121.4.c.j	$121$	$4$	121.c	11.c	$5$	$24$	$6$	$7.139$		None		✓	✓		121.4.a.h	$8$	$0$	\(0\)	\(-8\)	\(-14\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{4}^{\mathrm{old}}(121, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(121, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)