Space of modular forms of level 11, weight 9, and Character 11.d

• Label: 11.9.d
• Level: $11$
• Weight: $9$
• Character orbit: 11.d
• Rep. character: $\chi_{11}(2,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$11$
Weight:	$k$	$=$	$9$
Character orbit:	$[\chi]$	$=$	11.d (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$11$
Character field:			$\Q(\zeta_{10})$
Newform subspaces:			$1$
Sturm bound:			$9$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{9}(11, [\chi])$.

	Total	New	Old
Modular forms	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

Trace form

28 * q - 5 * q^2 + 144 * q^3 + 951 * q^4 - 708 * q^5 - 4485 * q^6 + 5470 * q^7 - 3845 * q^8 - 14225 * q^9 + 38567 * q^11 + 63954 * q^12 - 12500 * q^13 - 49262 * q^14 - 211056 * q^15 + 65335 * q^16 + 368200 * q^17 - 316350 * q^18 - 442685 * q^19 - 101488 * q^20 + 1686925 * q^22 + 704764 * q^23 - 426415 * q^24 - 960933 * q^25 + 659122 * q^26 - 1523847 * q^27 - 2014380 * q^28 - 795320 * q^29 + 680860 * q^30 + 1317554 * q^31 - 3224101 * q^33 + 897538 * q^34 + 8132260 * q^35 + 8527262 * q^36 + 8163354 * q^37 + 1456780 * q^38 - 14657890 * q^39 - 24701940 * q^40 - 13192700 * q^41 + 3806030 * q^42 - 8229340 * q^44 + 17701416 * q^45 + 38601510 * q^46 + 11954754 * q^47 + 49075784 * q^48 - 11198359 * q^49 - 41838705 * q^50 - 41019825 * q^51 - 81977530 * q^52 - 2537916 * q^53 + 40359452 * q^55 + 96646244 * q^56 + 88596375 * q^57 - 13252700 * q^58 + 49581537 * q^59 - 58912456 * q^60 - 29302910 * q^61 - 207755000 * q^62 - 178685550 * q^63 + 22221799 * q^64 + 119858070 * q^66 + 105502894 * q^67 + 335519000 * q^68 + 32103578 * q^69 + 228302300 * q^70 + 30044916 * q^71 - 375829355 * q^72 - 272936400 * q^73 - 400896650 * q^74 + 30339519 * q^75 + 23326180 * q^77 + 387475480 * q^78 + 319699810 * q^79 + 208513052 * q^80 + 403883776 * q^81 - 197581295 * q^82 - 558510965 * q^83 - 721672470 * q^84 - 360970180 * q^85 + 119645907 * q^86 + 85623835 * q^88 + 317966134 * q^89 + 1020614800 * q^90 + 285678712 * q^91 + 599604784 * q^92 - 125102972 * q^93 - 650361480 * q^94 - 641153840 * q^95 - 523100900 * q^96 + 85897149 * q^97 - 149389979 * q^99

Decomposition of $S_{9}^{\mathrm{new}}(11, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.9.d.a	$11$	$9$	11.d	11.d	$10$	$28$	$7$	$4.481$		None		✓	✓	✓	11.9.d.a	$2$	$0$	$-5$	$144$	$-708$	$5470$		$\mathrm{SU}(2)[C_{10}]$