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

• Label: 9.11.d
• Level: $9$
• Weight: $11$
• Character orbit: 9.d
• Rep. character: $\chi_{9}(2,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $11$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(11\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

18 * q - 3 * q^2 + 51 * q^3 + 4095 * q^4 + 4956 * q^5 - 5283 * q^6 - 6120 * q^7 - 3951 * q^9 - 2052 * q^10 + 969 * q^11 + 1031514 * q^12 + 140274 * q^13 - 2134578 * q^14 + 1174770 * q^15 - 1571841 * q^16 - 10430748 * q^18 + 2771370 * q^19 + 14542734 * q^20 + 7893876 * q^21 - 3475521 * q^22 - 9944382 * q^23 + 9173583 * q^24 + 14726277 * q^25 - 10369242 * q^27 - 22968324 * q^28 - 41383956 * q^29 - 67505382 * q^30 + 28428390 * q^31 + 165205143 * q^32 + 47221821 * q^33 - 66263103 * q^34 + 107351775 * q^36 + 63695196 * q^37 - 621662181 * q^38 - 161939274 * q^39 - 75566250 * q^40 + 452543883 * q^41 + 733154220 * q^42 + 102086037 * q^43 - 772291584 * q^45 + 44251488 * q^46 - 289445970 * q^47 - 411656979 * q^48 + 6735231 * q^49 + 1915252779 * q^50 + 1858869675 * q^51 + 19035576 * q^52 - 4488556437 * q^54 - 289455552 * q^55 - 4272894318 * q^56 - 1034132379 * q^57 - 83900178 * q^58 + 3065773551 * q^59 + 11567968038 * q^60 + 141349086 * q^61 - 4692569886 * q^63 - 28980486 * q^64 - 11094862926 * q^65 - 5862645990 * q^66 + 954074115 * q^67 + 21469701105 * q^68 + 11337524370 * q^69 - 1440686628 * q^70 - 12325971501 * q^72 + 772009902 * q^73 - 30101814978 * q^74 - 12481839489 * q^75 - 40906287 * q^76 + 25001072268 * q^77 + 31785497316 * q^78 + 2079634212 * q^79 - 14104914183 * q^81 - 1423292742 * q^82 - 23396438442 * q^83 - 15587763342 * q^84 - 5975304714 * q^85 + 39111097821 * q^86 + 39360802212 * q^87 + 2974531059 * q^88 - 56325384666 * q^90 + 2180413260 * q^91 - 40885098684 * q^92 + 709626342 * q^93 + 6395997924 * q^94 + 22335455946 * q^95 + 61717992336 * q^96 - 14510723337 * q^97 - 23929366734 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.11.d.a	$9$	$11$	9.d	9.d	$6$	$18$	$9$	$5.718$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓	✓	✓	9.11.d.a	$2$	$0$	\(-3\)	\(51\)	\(4956\)	\(-6120\)	$2^{14}\cdot 3^{36}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)