Space of modular forms of level 9, weight 4, and Character 9.c

• Label: 9.4.c
• Level: $9$
• Weight: $4$
• Character orbit: 9.c
• Rep. character: $\chi_{9}(4,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(9, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	4	4	0
Eisenstein series	4	4	0

Trace form

4 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 - 15 * q^5 + 9 * q^6 - 7 * q^7 + 66 * q^8 + 45 * q^9 + 12 * q^10 - 66 * q^11 - 156 * q^12 + 11 * q^13 - 60 * q^14 + 27 * q^15 + 7 * q^16 + 198 * q^17 + 216 * q^18 - 154 * q^19 + 12 * q^20 + 21 * q^21 + 33 * q^22 - 33 * q^23 - 99 * q^24 + 121 * q^25 - 528 * q^26 - 432 * q^27 + 332 * q^28 + 51 * q^29 + 288 * q^30 - 43 * q^31 + 423 * q^32 + 198 * q^33 - 297 * q^34 + 6 * q^35 - 225 * q^36 - 100 * q^37 + 561 * q^38 + 759 * q^39 - 264 * q^40 - 132 * q^41 - 486 * q^42 - 88 * q^43 - 462 * q^44 - 675 * q^45 - 528 * q^46 - 399 * q^47 - 21 * q^48 + 513 * q^49 + 429 * q^50 + 297 * q^51 + 770 * q^52 + 108 * q^53 + 1215 * q^54 + 1254 * q^55 - 66 * q^56 - 1221 * q^57 + 60 * q^58 - 798 * q^59 - 36 * q^60 - 439 * q^61 + 228 * q^62 + 603 * q^63 - 1454 * q^64 - 165 * q^65 - 990 * q^66 - 988 * q^67 - 693 * q^68 + 891 * q^69 - 318 * q^70 + 2736 * q^71 + 891 * q^72 - 910 * q^73 - 816 * q^74 - 363 * q^75 + 1529 * q^76 + 165 * q^77 - 990 * q^78 + 803 * q^79 + 192 * q^80 - 567 * q^81 + 3630 * q^82 - 813 * q^83 + 642 * q^84 - 594 * q^85 - 33 * q^86 - 153 * q^87 - 1221 * q^88 - 792 * q^89 - 756 * q^90 - 1562 * q^91 + 858 * q^92 - 213 * q^93 - 2100 * q^94 + 132 * q^95 + 1080 * q^96 - 736 * q^97 - 846 * q^98 + 297 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.4.c.a	$9$	$4$	9.c	9.c	$3$	$4$	$2$	$0.531$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓	✓	✓	9.4.c.a	$2$	$0$	\(-3\)	\(-3\)	\(-15\)	\(-7\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)