Newform orbit 91.2.ba.a

• Label: 91.2.ba.a
• Level: $91$
• Weight: $2$
• Character orbit: 91.ba
• Analytic conductor: $0.727$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.ba (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.726638658394\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(7\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 12 q^{6} - 6 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
45.1	−1.56744	+	1.56744i	0.959879	−	0.554186i		−	2.91373i	−0.784926	+	2.92938i	−0.635898	+	2.37321i	2.25305	+	1.38700i	1.43221	+	1.43221i	−0.885755	+	1.53417i	−3.36131	−	5.82195i
45.2	−0.984398	+	0.984398i	−1.25446	+	0.724265i			0.0619199i	−0.172312	+	0.643078i	0.521927	−	1.94786i	−2.46519	−	0.960657i	−2.02975	−	2.02975i	−0.450880	+	0.780947i	−0.463421	−	0.802669i
45.3	−0.270646	+	0.270646i	0.792292	−	0.457430i			1.85350i	0.959617	−	3.58134i	−0.0906291	+	0.338232i	1.30385	+	2.30217i	−1.04293	−	1.04293i	−1.08152	+	1.87324i	0.709559	+	1.22899i
45.4	−0.193244	+	0.193244i	2.17048	−	1.25313i			1.92531i	−0.383199	+	1.43012i	−0.177273	+	0.661591i	−2.15474	−	1.53528i	−0.758543	−	0.758543i	1.64065	−	2.84169i	−0.202311	−	0.350412i
45.5	0.490988	−	0.490988i	−2.71085	+	1.56511i			1.51786i	−0.00962681	+	0.0359277i	−0.562545	+	2.09944i	−0.176775	+	2.63984i	1.72723	+	1.72723i	3.39913	−	5.88747i	0.0129135	+	0.0223668i
45.6	1.14693	−	1.14693i	−0.445073	+	0.256963i		−	0.630890i	0.395109	−	1.47457i	−0.215749	+	0.805186i	0.0531605	−	2.64522i	1.57027	+	1.57027i	−1.36794	+	2.36934i	−1.23806	−	2.14439i
45.7	1.74384	−	1.74384i	−0.146239	+	0.0844309i		−	4.08193i	−0.638637	+	2.38343i	−0.107782	+	0.402250i	−2.04541	+	1.67818i	−3.63054	−	3.63054i	−1.48574	+	2.57338i	3.04263	+	5.26998i
54.1	−1.72056	+	1.72056i	−1.70689	−	0.985473i		−	3.92067i	0.227080	−	0.0608458i	4.63238	−	1.24124i	1.27342	−	2.31914i	3.30464	+	3.30464i	0.442313	+	0.766108i	−0.286016	+	0.495394i
54.2	−1.42500	+	1.42500i	1.25027	+	0.721843i		−	2.06123i	3.16920	−	0.849184i	−2.81025	+	0.753004i	−0.111396	+	2.64341i	0.0872533	+	0.0872533i	−0.457887	−	0.793083i	−3.30601	+	5.72618i
54.3	−0.876516	+	0.876516i	1.92717	+	1.11265i			0.463441i	−2.51660	+	0.674321i	−2.66446	+	0.713939i	2.20101	−	1.46818i	−2.15924	−	2.15924i	0.975997	+	1.69048i	1.61479	−	2.79689i
54.4	−0.347096	+	0.347096i	−2.11812	−	1.22290i			1.75905i	−3.47544	+	0.931242i	1.15965	−	0.310728i	0.701045	+	2.55118i	−1.30475	−	1.30475i	1.49096	+	2.58241i	0.883082	−	1.52954i
54.5	0.203761	−	0.203761i	0.923129	+	0.532969i			1.91696i	0.499383	−	0.133809i	0.296695	−	0.0794993i	−2.60732	−	0.449339i	0.798123	+	0.798123i	−0.931889	−	1.61408i	0.0744896	−	0.129020i
54.6	1.28453	−	1.28453i	−2.65867	−	1.53499i		−	1.30006i	1.07541	−	0.288156i	−5.38690	+	1.44342i	−0.978346	−	2.45822i	0.899098	+	0.899098i	3.21237	+	5.56398i	1.01126	−	1.75155i
54.7	1.51485	−	1.51485i	0.0170886	+	0.00986613i		−	2.58954i	−1.34505	+	0.360406i	0.0408324	−	0.0109410i	−0.246373	+	2.63426i	−0.893066	−	0.893066i	−1.49981	−	2.59774i	−1.49159	+	2.58351i
59.1	−1.72056	−	1.72056i	−1.70689	+	0.985473i			3.92067i	0.227080	+	0.0608458i	4.63238	+	1.24124i	1.27342	+	2.31914i	3.30464	−	3.30464i	0.442313	−	0.766108i	−0.286016	−	0.495394i
59.2	−1.42500	−	1.42500i	1.25027	−	0.721843i			2.06123i	3.16920	+	0.849184i	−2.81025	−	0.753004i	−0.111396	−	2.64341i	0.0872533	−	0.0872533i	−0.457887	+	0.793083i	−3.30601	−	5.72618i
59.3	−0.876516	−	0.876516i	1.92717	−	1.11265i		−	0.463441i	−2.51660	−	0.674321i	−2.66446	−	0.713939i	2.20101	+	1.46818i	−2.15924	+	2.15924i	0.975997	−	1.69048i	1.61479	+	2.79689i
59.4	−0.347096	−	0.347096i	−2.11812	+	1.22290i		−	1.75905i	−3.47544	−	0.931242i	1.15965	+	0.310728i	0.701045	−	2.55118i	−1.30475	+	1.30475i	1.49096	−	2.58241i	0.883082	+	1.52954i
59.5	0.203761	+	0.203761i	0.923129	−	0.532969i		−	1.91696i	0.499383	+	0.133809i	0.296695	+	0.0794993i	−2.60732	+	0.449339i	0.798123	−	0.798123i	−0.931889	+	1.61408i	0.0744896	+	0.129020i
59.6	1.28453	+	1.28453i	−2.65867	+	1.53499i			1.30006i	1.07541	+	0.288156i	−5.38690	−	1.44342i	−0.978346	+	2.45822i	0.899098	−	0.899098i	3.21237	−	5.56398i	1.01126	+	1.75155i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
91.ba	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	91.2.ba.a	yes	28
3.b	odd	2	1		819.2.et.b		28
7.b	odd	2	1		637.2.bb.a		28
7.c	even	3	1		637.2.x.a		28
7.c	even	3	1		637.2.bd.b		28
7.d	odd	6	1		91.2.w.a	✓	28
7.d	odd	6	1		637.2.bd.a		28
13.f	odd	12	1		91.2.w.a	✓	28
21.g	even	6	1		819.2.gh.b		28
39.k	even	12	1		819.2.gh.b		28
91.w	even	12	1		637.2.bd.b		28
91.x	odd	12	1		637.2.bb.a		28
91.ba	even	12	1	inner	91.2.ba.a	yes	28
91.bc	even	12	1		637.2.x.a		28
91.bd	odd	12	1		637.2.bd.a		28
273.bs	odd	12	1		819.2.et.b		28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.2.w.a	✓	28	7.d	odd	6	1
91.2.w.a	✓	28	13.f	odd	12	1
91.2.ba.a	yes	28	1.a	even	1	1	trivial
91.2.ba.a	yes	28	91.ba	even	12	1	inner
637.2.x.a		28	7.c	even	3	1
637.2.x.a		28	91.bc	even	12	1
637.2.bb.a		28	7.b	odd	2	1
637.2.bb.a		28	91.x	odd	12	1
637.2.bd.a		28	7.d	odd	6	1
637.2.bd.a		28	91.bd	odd	12	1
637.2.bd.b		28	7.c	even	3	1
637.2.bd.b		28	91.w	even	12	1
819.2.et.b		28	3.b	odd	2	1
819.2.et.b		28	273.bs	odd	12	1
819.2.gh.b		28	21.g	even	6	1
819.2.gh.b		28	39.k	even	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(91, [\chi])\).