Space of modular forms of level 3, weight 9, and Character 3.b

• Label: 3.9.b
• Level: $3$
• Weight: $9$
• Character orbit: 3.b
• Rep. character: $\chi_{3}(2,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(3, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

2 * q + 90 * q^3 - 496 * q^4 + 3024 * q^6 - 3500 * q^7 - 5022 * q^9 + 10080 * q^10 - 22320 * q^12 + 51460 * q^13 - 30240 * q^15 - 135040 * q^16 + 272160 * q^18 + 37876 * q^19 - 157500 * q^21 - 312480 * q^22 + 24192 * q^24 + 680450 * q^25 - 1042470 * q^27 + 868000 * q^28 + 453600 * q^30 - 702956 * q^31 + 937440 * q^33 - 3362688 * q^34 + 1245456 * q^36 + 2670340 * q^37 + 2315700 * q^39 + 80640 * q^40 - 5292000 * q^42 - 7052300 * q^43 - 2721600 * q^45 + 21123648 * q^46 - 6076800 * q^48 - 5404602 * q^49 + 10088064 * q^51 - 12762080 * q^52 + 4653936 * q^54 + 3124800 * q^55 + 1704420 * q^57 - 20694240 * q^58 + 7499520 * q^60 + 1507204 * q^61 + 8788500 * q^63 + 31425536 * q^64 - 14061600 * q^66 + 4537780 * q^67 - 63370944 * q^69 - 17640000 * q^70 + 2177280 * q^72 + 55345540 * q^73 + 30620250 * q^75 - 9393248 * q^76 + 77807520 * q^78 - 45961964 * q^79 - 60872958 * q^81 - 84208320 * q^82 + 39060000 * q^84 + 33626880 * q^85 + 62082720 * q^87 - 2499840 * q^88 - 25310880 * q^90 - 90055000 * q^91 - 31633020 * q^93 + 183238272 * q^94 - 197987328 * q^96 + 294542020 * q^97 + 84369600 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(3, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.9.b.a	$3$	$9$	3.b	3.b	$2$	$2$	$2$	$1.222$	\(\Q(\sqrt{-14}) \)	None		✓	✓	✓	3.9.b.a	$2$	$0$	\(0\)	\(90\)	\(0\)	\(-3500\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots\)