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

• Label: 9.9.d
• Level: $9$
• Weight: $9$
• Character orbit: 9.d
• Rep. character: $\chi_{9}(2,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
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:			\(9\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	18	18	0
Cusp forms	14	14	0
Eisenstein series	4	4	0

Trace form

14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.9.d.a	$9$	$9$	9.d	9.d	$6$	$14$	$7$	$3.666$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓	✓	9.9.d.a	$2$	$0$	\(-3\)	\(-93\)	\(438\)	\(922\)	$2^{6}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots\)