Newform orbit 189.2.v.a

• Label: 189.2.v.a
• Level: $189$
• Weight: $2$
• Character orbit: 189.v
• Analytic conductor: $1.509$
• Analytic rank: $0$
• Dimension: $54$
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$189 = 3^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	189.v (of order $9$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

Label	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
22.1	−1.88664	+	1.58308i	0.279041	−	1.70943i	0.705975	−	4.00378i	−1.28676	+	0.468343i	2.17970	+	3.66681i	0.173648	+	0.984808i	2.54355	+	4.40555i	−2.84427	−	0.954001i	1.68623	−	2.92064i
22.2	−1.17963	+	0.989828i	0.853595	+	1.50711i	0.0644735	−	0.365648i	−1.99174	+	0.724932i	−2.49871	−	0.932919i	0.173648	+	0.984808i	−1.25403	−	2.17204i	−1.54275	+	2.57292i	1.63195	−	2.82663i
22.3	−1.09798	+	0.921318i	−1.39977	−	1.02012i	0.00944557	−	0.0535685i	1.35272	−	0.492351i	2.47678	−	0.169559i	0.173648	+	0.984808i	−1.39433	−	2.41506i	0.918713	+	2.85587i	−1.03166	+	1.78688i
22.4	0.0808704	−	0.0678583i	1.71585	−	0.236354i	−0.345361	+	1.95864i	0.0449304	−	0.0163533i	0.122723	−	0.135549i	0.173648	+	0.984808i	0.210549	+	0.364682i	2.88827	−	0.811094i	0.00252383	−	0.00437140i
22.5	0.731503	−	0.613803i	−1.57520	−	0.720230i	−0.188955	+	1.07162i	−3.78665	+	1.37823i	−1.59435	+	0.440016i	0.173648	+	0.984808i	1.47445	+	2.55382i	1.96254	+	2.26902i	−1.92398	+	3.33244i
22.6	0.786541	−	0.659987i	−0.244375	−	1.71472i	−0.164231	+	0.931402i	3.56827	−	1.29874i	−1.32391	−	1.18742i	0.173648	+	0.984808i	1.51229	+	2.61937i	−2.88056	+	0.838073i	1.94944	−	3.37653i
22.7	0.969537	−	0.813538i	−0.430185	+	1.67778i	−0.0691389	+	0.392106i	−0.855069	+	0.311220i	0.947857	+	1.97664i	0.173648	+	0.984808i	1.51760	+	2.62856i	−2.62988	−	1.44351i	−0.575832	+	0.997370i
22.8	1.89179	−	1.58740i	−1.45321	+	0.942429i	0.711733	−	4.03644i	2.16637	−	0.788496i	−1.25316	+	4.08971i	0.173648	+	0.984808i	−2.59144	−	4.48850i	1.22366	−	2.73910i	2.84667	−	4.93057i
22.9	2.00215	−	1.68000i	1.58061	+	0.708280i	0.838893	−	4.75760i	−3.29720	+	1.20008i	4.35453	−	1.23735i	0.173648	+	0.984808i	−3.69957	−	6.40784i	1.99668	+	2.23903i	−4.58534	+	7.94204i
43.1	−1.88664	−	1.58308i	0.279041	+	1.70943i	0.705975	+	4.00378i	−1.28676	−	0.468343i	2.17970	−	3.66681i	0.173648	−	0.984808i	2.54355	−	4.40555i	−2.84427	+	0.954001i	1.68623	+	2.92064i
43.2	−1.17963	−	0.989828i	0.853595	−	1.50711i	0.0644735	+	0.365648i	−1.99174	−	0.724932i	−2.49871	+	0.932919i	0.173648	−	0.984808i	−1.25403	+	2.17204i	−1.54275	−	2.57292i	1.63195	+	2.82663i
43.3	−1.09798	−	0.921318i	−1.39977	+	1.02012i	0.00944557	+	0.0535685i	1.35272	+	0.492351i	2.47678	+	0.169559i	0.173648	−	0.984808i	−1.39433	+	2.41506i	0.918713	−	2.85587i	−1.03166	−	1.78688i
43.4	0.0808704	+	0.0678583i	1.71585	+	0.236354i	−0.345361	−	1.95864i	0.0449304	+	0.0163533i	0.122723	+	0.135549i	0.173648	−	0.984808i	0.210549	−	0.364682i	2.88827	+	0.811094i	0.00252383	+	0.00437140i
43.5	0.731503	+	0.613803i	−1.57520	+	0.720230i	−0.188955	−	1.07162i	−3.78665	−	1.37823i	−1.59435	−	0.440016i	0.173648	−	0.984808i	1.47445	−	2.55382i	1.96254	−	2.26902i	−1.92398	−	3.33244i
43.6	0.786541	+	0.659987i	−0.244375	+	1.71472i	−0.164231	−	0.931402i	3.56827	+	1.29874i	−1.32391	+	1.18742i	0.173648	−	0.984808i	1.51229	−	2.61937i	−2.88056	−	0.838073i	1.94944	+	3.37653i
43.7	0.969537	+	0.813538i	−0.430185	−	1.67778i	−0.0691389	−	0.392106i	−0.855069	−	0.311220i	0.947857	−	1.97664i	0.173648	−	0.984808i	1.51760	−	2.62856i	−2.62988	+	1.44351i	−0.575832	−	0.997370i
43.8	1.89179	+	1.58740i	−1.45321	−	0.942429i	0.711733	+	4.03644i	2.16637	+	0.788496i	−1.25316	−	4.08971i	0.173648	−	0.984808i	−2.59144	+	4.48850i	1.22366	+	2.73910i	2.84667	+	4.93057i
43.9	2.00215	+	1.68000i	1.58061	−	0.708280i	0.838893	+	4.75760i	−3.29720	−	1.20008i	4.35453	+	1.23735i	0.173648	−	0.984808i	−3.69957	+	6.40784i	1.99668	−	2.23903i	−4.58534	−	7.94204i
85.1	−2.52562	−	0.919249i	1.69786	+	0.342450i	4.00163	+	3.35776i	0.203200	−	1.15240i	−3.97334	−	2.42565i	0.766044	−	0.642788i	−4.33224	−	7.50367i	2.76546	+	1.16287i	−1.57255	+	2.72374i
85.2	−2.17921	−	0.793168i	−1.72903	−	0.102202i	2.58775	+	2.17138i	0.443161	−	2.51329i	3.68686	+	1.59413i	0.766044	−	0.642788i	−1.59792	−	2.76768i	2.97911	+	0.353421i	−2.95920	+	5.12549i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
27.e	even	9	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	189.2.v.a	✓	54
3.b	odd	2	1		567.2.v.b		54
27.e	even	9	1	inner	189.2.v.a	✓	54
27.e	even	9	1		5103.2.a.i		27
27.f	odd	18	1		567.2.v.b		54
27.f	odd	18	1		5103.2.a.f		27

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
189.2.v.a	✓	54	1.a	even	1	1	trivial
189.2.v.a	✓	54	27.e	even	9	1	inner
567.2.v.b		54	3.b	odd	2	1
567.2.v.b		54	27.f	odd	18	1
5103.2.a.f		27	27.f	odd	18	1
5103.2.a.i		27	27.e	even	9	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^54 + 21*T2^51 - 27*T2^49 + 612*T2^48 + 117*T2^47 - 648*T2^46 + 4353*T2^45 + 2295*T2^44 - 12726*T2^43 + 107883*T2^42 + 23976*T2^41 - 101034*T2^40 + 629919*T2^39 - 77058*T2^38 - 711450*T2^37 + 13634181*T2^36 - 2427651*T2^35 + 3313980*T2^34 + 20904210*T2^33 - 55368522*T2^32 - 46332243*T2^31 + 384642162*T2^30 - 119824029*T2^29 + 561003651*T2^28 + 434738799*T2^27 - 95898249*T2^26 - 2245963707*T2^25 + 8716351032*T2^24 - 5691287691*T2^23 + 1201657599*T2^22 + 3158848854*T2^21 + 7037497971*T2^20 - 25426610208*T2^19 + 33160184271*T2^18 - 6122042856*T2^17 - 18471601989*T2^16 + 13364522019*T2^15 + 8511132591*T2^14 - 34005747564*T2^13 + 58498460901*T2^12 - 54860230881*T2^11 + 23940434358*T2^10 - 845763444*T2^9 - 2028766176*T2^8 + 179520624*T2^7 + 67450725*T2^6 + 3300183*T2^5 + 7018083*T2^4 - 888651*T2^3 + 104976*T2^2 - 6561*T2 + 729