Space of modular forms of level 9, weight 7, and Character 9.d

• Label: 9.7.d
• Level: $9$
• Weight: $7$
• Character orbit: 9.d
• Rep. character: $\chi_{9}(2,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(7\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(9, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

Trace form

10 * q - 3 * q^2 + 24 * q^3 + 127 * q^4 - 219 * q^5 + 333 * q^6 - 121 * q^7 - 1980 * q^9 - 132 * q^10 + 483 * q^11 - 1830 * q^12 - 841 * q^13 + 12174 * q^14 + 7965 * q^15 - 1985 * q^16 - 7884 * q^18 + 6176 * q^19 - 63186 * q^20 - 25845 * q^21 + 3471 * q^22 + 53565 * q^23 + 111519 * q^24 + 8452 * q^25 - 101034 * q^27 - 22660 * q^28 - 80679 * q^29 - 37782 * q^30 - 24601 * q^31 + 218295 * q^32 + 229995 * q^33 + 7425 * q^34 - 274977 * q^36 + 12764 * q^37 - 371877 * q^38 - 112749 * q^39 + 54150 * q^40 + 232251 * q^41 + 270540 * q^42 - 93271 * q^43 + 63801 * q^45 + 112512 * q^46 - 142887 * q^47 - 143283 * q^48 + 86238 * q^49 + 318459 * q^50 + 57078 * q^51 + 186920 * q^52 + 13851 * q^54 - 419982 * q^55 + 342546 * q^56 - 1086 * q^57 - 380658 * q^58 - 995061 * q^59 - 1011402 * q^60 - 59305 * q^61 + 526455 * q^63 + 403066 * q^64 + 1642029 * q^65 + 1610586 * q^66 + 158513 * q^67 - 1693791 * q^68 - 851715 * q^69 - 304788 * q^70 + 1469907 * q^72 + 933896 * q^73 + 595182 * q^74 - 757524 * q^75 + 666641 * q^76 - 2198883 * q^77 - 3481884 * q^78 + 468707 * q^79 + 1774548 * q^81 - 2038470 * q^82 + 3008337 * q^83 + 1543746 * q^84 - 1189944 * q^85 + 1905549 * q^86 - 615591 * q^87 - 349773 * q^88 + 84294 * q^90 - 211778 * q^91 - 973788 * q^92 - 2954553 * q^93 + 809124 * q^94 - 2562954 * q^95 - 1022112 * q^96 + 336029 * q^97 - 432567 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.7.d.a	$9$	$7$	9.d	9.d	$6$	$10$	$5$	$2.070$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓	✓	9.7.d.a	$2$	$0$	\(-3\)	\(24\)	\(-219\)	\(-121\)	$2^{2}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots\)