Space of modular forms of level 55, weight 6, and Character 55.g

• Label: 55.6.g
• Level: $55$
• Weight: $6$
• Character orbit: 55.g
• Rep. character: $\chi_{55}(16,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	55.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(55, [\chi])\).

	Total	New	Old
Modular forms	128	80	48
Cusp forms	112	80	32
Eisenstein series	16	0	16

Trace form

80 * q - 4 * q^2 + 44 * q^3 - 276 * q^4 + 24 * q^6 - 196 * q^7 - 932 * q^8 - 1158 * q^9 + 800 * q^10 + 1038 * q^11 + 2112 * q^12 - 1282 * q^13 + 942 * q^14 - 1650 * q^15 - 11032 * q^16 - 1108 * q^17 - 574 * q^18 + 4262 * q^19 + 1900 * q^20 + 1408 * q^21 + 26404 * q^22 + 4568 * q^23 - 6604 * q^24 - 12500 * q^25 - 15820 * q^26 - 46420 * q^27 - 17618 * q^28 - 14634 * q^29 + 8000 * q^30 + 9996 * q^31 + 96252 * q^32 + 39434 * q^33 + 61004 * q^34 - 12700 * q^35 - 91632 * q^36 - 40108 * q^37 - 49794 * q^38 - 31738 * q^39 - 9600 * q^40 + 25584 * q^41 + 160282 * q^42 + 56276 * q^43 + 126246 * q^44 - 102138 * q^46 + 36116 * q^47 + 46734 * q^48 - 91870 * q^49 - 2500 * q^50 + 19414 * q^51 - 52706 * q^52 - 126976 * q^53 - 98904 * q^54 - 53700 * q^55 - 261248 * q^56 + 200550 * q^57 - 100706 * q^58 - 13830 * q^59 + 58850 * q^60 + 58988 * q^61 + 293648 * q^62 + 88834 * q^63 - 115960 * q^64 + 154600 * q^65 + 371866 * q^66 - 226520 * q^67 + 161574 * q^68 - 140082 * q^69 - 23200 * q^70 + 178196 * q^71 + 388974 * q^72 - 226830 * q^73 - 353200 * q^74 - 41250 * q^75 - 1077952 * q^76 - 212966 * q^77 - 12876 * q^78 - 131282 * q^79 + 133400 * q^80 + 229356 * q^81 + 58620 * q^82 - 93062 * q^83 + 323208 * q^84 - 46600 * q^85 + 545604 * q^86 - 67148 * q^87 - 1409056 * q^88 - 82224 * q^89 + 61400 * q^90 + 372216 * q^91 + 140088 * q^92 + 875648 * q^93 + 198480 * q^94 - 144400 * q^95 - 138942 * q^96 - 209016 * q^97 + 1260268 * q^98 - 876496 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(55, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.6.g.a	$55$	$6$	55.g	11.c	$5$	$40$	$10$	$8.821$		None		✓			55.6.g.a	$2$	$0$	\(-6\)	\(-11\)	\(-250\)	\(-207\)		$\mathrm{SU}(2)[C_{5}]$
55.6.g.b	$55$	$6$	55.g	11.c	$5$	$40$	$10$	$8.821$		None		✓			55.6.g.b	$2$	$0$	\(2\)	\(55\)	\(250\)	\(11\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{6}^{\mathrm{old}}(55, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(55, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)