Space of modular forms of level 9, weight 5, and Character 9.d

• Label: 9.5.d
• Level: $9$
• Weight: $5$
• Character orbit: 9.d
• Rep. character: $\chi_{9}(2,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(9, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

Trace form

6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9 - 36 * q^10 + 483 * q^11 + 330 * q^12 - 6 * q^13 - 1146 * q^14 - 1026 * q^15 + 15 * q^16 + 1404 * q^18 - 258 * q^19 + 1614 * q^20 + 480 * q^21 - 369 * q^22 - 282 * q^23 - 1449 * q^24 - 273 * q^25 + 54 * q^27 + 1308 * q^28 - 1056 * q^29 - 1278 * q^30 + 1290 * q^31 - 1161 * q^32 + 279 * q^33 + 513 * q^34 - 2385 * q^36 + 12 * q^37 - 789 * q^38 + 1974 * q^39 - 1314 * q^40 + 7629 * q^41 + 9612 * q^42 - 285 * q^43 - 4212 * q^45 - 5760 * q^46 - 9642 * q^47 - 6771 * q^48 - 1863 * q^49 + 3027 * q^50 + 2457 * q^51 - 240 * q^52 - 405 * q^54 + 2016 * q^55 - 462 * q^56 + 5367 * q^57 + 6462 * q^58 + 6225 * q^59 + 7470 * q^60 + 3630 * q^61 - 7578 * q^63 + 15450 * q^64 - 7158 * q^65 - 13734 * q^66 - 5055 * q^67 - 10503 * q^68 - 13878 * q^69 - 9684 * q^70 + 8451 * q^72 - 14622 * q^73 + 26454 * q^74 + 21021 * q^75 - 4047 * q^76 + 2580 * q^77 - 12060 * q^78 + 4764 * q^79 + 18387 * q^81 - 9702 * q^82 - 1866 * q^83 - 6486 * q^84 + 12366 * q^85 - 37731 * q^86 - 21564 * q^87 + 14787 * q^88 + 20790 * q^90 + 34836 * q^91 + 33636 * q^92 + 19254 * q^93 - 12708 * q^94 - 13362 * q^95 - 3672 * q^96 - 28959 * q^97 - 9126 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.5.d.a	$9$	$5$	9.d	9.d	$6$	$6$	$3$	$0.930$	6.0.39400128.1	None		✓	✓	✓	9.5.d.a	$2$	$0$	\(-3\)	\(-3\)	\(-12\)	\(12\)	$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)