Newform orbit 889.2.bm.a

• Label: 889.2.bm.a
• Level: $889$
• Weight: $2$
• Character orbit: 889.bm
• Analytic conductor: $7.099$
• Analytic rank: $0$
• Dimension: $1008$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.bm (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.09870073969\)
Analytic rank:	\(0\)
Dimension:	\(1008\)
Relative dimension:	\(84\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 1008 q - 7 q^{3} + 84 q^{4} - 9 q^{5} - 28 q^{6} - 19 q^{7} - 30 q^{8} + 67 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−2.29271	+	1.56315i	−0.432440	+	0.133390i	2.08243	−	5.30595i	1.45884	+	3.71706i	0.782953	−	0.981791i	−1.20810	+	2.35383i	2.28462	+	10.0096i	−2.30951	+	1.57459i	−9.15500	−	6.24178i
2.2	−2.24716	+	1.53208i	2.47407	−	0.763151i	1.97174	−	5.02392i	0.313611	+	0.799068i	−4.39042	+	5.50541i	−1.53616	−	2.15412i	2.05586	+	9.00731i	3.05993	−	2.08622i	−1.92897	−	1.31515i
2.3	−2.24110	+	1.52796i	−2.03600	+	0.628021i	1.95721	−	4.98688i	0.0276021	+	0.0703289i	3.60329	−	4.51838i	2.62302	−	0.346077i	2.02631	+	8.87783i	1.27215	−	0.867338i	−0.169319	−	0.115440i
2.4	−2.22661	+	1.51808i	1.18236	−	0.364711i	1.92255	−	4.89859i	−0.739876	−	1.88517i	−2.07900	+	2.60699i	2.62062	+	0.363782i	1.95632	+	8.57121i	−1.21375	+	0.827519i	4.50926	+	3.07436i
2.5	−2.16445	+	1.47569i	0.580684	−	0.179117i	1.77647	−	4.52638i	−1.07747	−	2.74534i	−0.992538	+	1.24460i	−2.37649	+	1.16287i	1.66862	+	7.31071i	−2.17361	+	1.48194i	6.38340	+	4.35213i
2.6	−1.99439	+	1.35975i	−1.41270	+	0.435760i	1.39798	−	3.56201i	−0.566510	−	1.44344i	2.22495	−	2.79000i	−2.63380	+	0.251165i	0.981069	+	4.29834i	−0.672884	+	0.458765i	3.09257	+	2.10848i
2.7	−1.99235	+	1.35836i	−1.95808	+	0.603988i	1.39364	−	3.55093i	0.536874	+	1.36793i	3.08075	−	3.86314i	−0.975234	−	2.45946i	0.973686	+	4.26600i	0.990559	−	0.675352i	−2.92779	−	1.99613i
2.8	−1.94497	+	1.32606i	−1.95992	+	0.604554i	1.29380	−	3.29656i	−1.27798	−	3.25625i	3.01031	−	3.77481i	0.266202	−	2.63233i	0.807389	+	3.53740i	0.997068	−	0.679789i	6.80363	+	4.63863i
2.9	−1.91528	+	1.30581i	2.77906	−	0.857225i	1.23246	−	3.14025i	0.974845	+	2.48386i	−4.20329	+	5.27076i	2.05527	+	1.66610i	0.708446	+	3.10391i	4.50960	−	3.07459i	−5.11056	−	3.48432i
2.10	−1.86825	+	1.27375i	1.01989	−	0.314595i	1.13724	−	2.89764i	0.0791032	+	0.201552i	−1.50470	+	1.88683i	1.54163	+	2.15021i	0.559919	+	2.45317i	−1.53751	+	1.04826i	−0.404512	−	0.275792i
2.11	−1.86819	+	1.27371i	0.347581	−	0.107215i	1.13711	−	2.89732i	0.697525	+	1.77726i	−0.512788	+	0.643015i	1.79933	−	1.93969i	0.559726	+	2.45232i	−2.36940	+	1.61543i	−3.56683	−	2.43182i
2.12	−1.78079	+	1.21412i	1.63216	−	0.503453i	0.966433	−	2.46243i	−0.616556	−	1.57096i	−2.29527	+	2.87818i	−0.986896	−	2.45480i	0.309480	+	1.35592i	−0.0682486	+	0.0465311i	3.00529	+	2.04897i
2.13	−1.77049	+	1.20710i	−2.85314	+	0.880077i	0.946870	−	2.41259i	0.746048	+	1.90090i	3.98912	−	5.00220i	−0.476374	+	2.60251i	0.282158	+	1.23622i	4.88715	−	3.33200i	−3.61545	−	2.46497i
2.14	−1.73594	+	1.18354i	−1.77532	+	0.547615i	0.882028	−	2.24737i	0.0270140	+	0.0688306i	2.43373	−	3.05180i	0.776326	+	2.52929i	0.193674	+	0.848541i	0.373178	−	0.254429i	−0.128359	−	0.0875135i
2.15	−1.70914	+	1.16527i	3.12972	−	0.965389i	0.832621	−	2.12148i	−1.38812	−	3.53687i	−4.22418	+	5.29696i	−1.35291	+	2.27368i	0.128436	+	0.562713i	6.38443	−	4.35283i	6.49391	+	4.42747i
2.16	−1.54722	+	1.05488i	2.08149	−	0.642055i	0.550441	−	1.40250i	1.35100	+	3.44230i	−2.54323	+	3.18911i	−2.63698	+	0.215257i	−0.205575	−	0.900685i	1.44165	−	0.982903i	−5.72150	−	3.90085i
2.17	−1.50493	+	1.02604i	2.90080	−	0.894778i	0.481359	−	1.22648i	−0.293729	−	0.748408i	−3.44741	+	4.32291i	1.67430	−	2.04859i	−0.276595	−	1.21184i	5.13529	−	3.50118i	1.20994	+	0.824921i
2.18	−1.48042	+	1.00933i	0.840000	−	0.259106i	0.442205	−	1.12672i	−0.0525696	−	0.133945i	−0.982027	+	1.23142i	−1.99509	+	1.73771i	−0.314820	−	1.37932i	−1.84025	+	1.25466i	0.213020	+	0.145235i
2.19	−1.43575	+	0.978878i	−0.585131	+	0.180489i	0.372495	−	0.949103i	−1.46039	−	3.72101i	0.663425	−	0.831909i	1.56567	+	2.13276i	−0.379101	−	1.66095i	−2.16891	+	1.47874i	5.73917	+	3.91290i
2.20	−1.39346	+	0.950047i	−2.63632	+	0.813197i	0.308467	−	0.785962i	1.32085	+	3.36547i	2.90104	−	3.63779i	0.616339	−	2.57296i	−0.433706	−	1.90019i	3.81017	−	2.59773i	−5.03791	−	3.43479i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner
127.e	even	7	1	inner
889.bm	even	21	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	889.2.bm.a	✓	1008
7.c	even	3	1	inner	889.2.bm.a	✓	1008
127.e	even	7	1	inner	889.2.bm.a	✓	1008
889.bm	even	21	1	inner	889.2.bm.a	✓	1008

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
889.2.bm.a	✓	1008	1.a	even	1	1	trivial
889.2.bm.a	✓	1008	7.c	even	3	1	inner
889.2.bm.a	✓	1008	127.e	even	7	1	inner
889.2.bm.a	✓	1008	889.bm	even	21	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(889, [\chi])\).