Newform orbit 112.2.v.a

• Label: 112.2.v.a
• Level: $112$
• Weight: $2$
• Character orbit: 112.v
• Analytic conductor: $0.894$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.894324502638\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(14\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.41419	−	0.00846089i	1.95777	−	0.524583i	1.99986	+	0.0239306i	0.666898	−	2.48890i	−2.77309	+	0.725295i	−2.38027	+	1.15512i	−2.82797	−	0.0507629i	0.959602	−	0.554026i	−0.964178	+	3.51413i
3.2	−1.25731	−	0.647437i	−3.08091	+	0.825526i	1.16165	+	1.62806i	0.501060	−	1.86998i	4.40813	+	0.956753i	2.17953	+	1.49988i	−0.406487	−	2.79907i	6.21241	−	3.58674i	−1.84068	+	2.02674i
3.3	−1.25445	+	0.652965i	−1.05433	+	0.282507i	1.14727	−	1.63822i	−0.374919	+	1.39922i	1.13814	−	1.04283i	−0.298614	+	2.62885i	−0.369496	+	2.80419i	−1.56627	+	0.904287i	−0.443324	−	2.00005i
3.4	−0.946521	+	1.05076i	2.77508	−	0.743580i	−0.208197	−	1.98913i	−0.907491	+	3.38680i	−1.84535	+	3.61976i	0.0791552	−	2.64457i	2.28717	+	1.66399i	4.55008	−	2.62699i	−2.69976	−	4.15923i
3.5	−0.910025	−	1.08252i	1.67893	−	0.449868i	−0.343708	+	1.97024i	0.195879	−	0.731029i	−2.01486	−	1.40809i	2.52163	−	0.800849i	2.44562	−	1.42090i	0.0183525	−	0.0105958i	−0.969610	+	0.453212i
3.6	−0.799555	−	1.16650i	−0.763582	+	0.204601i	−0.721425	+	1.86535i	−1.02188	+	3.81370i	0.849192	+	0.727125i	−2.64575	+	0.00379639i	2.75275	−	0.649913i	−2.05688	+	1.18754i	5.26571	−	1.85724i
3.7	−0.252874	+	1.39142i	−2.61463	+	0.700587i	−1.87211	−	0.703710i	0.120751	−	0.450647i	−0.313640	−	3.81521i	−2.37326	−	1.16946i	1.45257	−	2.42694i	3.74737	−	2.16355i	0.596506	+	0.281972i
3.8	0.149759	−	1.40626i	−1.44888	+	0.388227i	−1.95514	−	0.421199i	0.755106	−	2.81809i	0.328966	+	2.09565i	−1.47726	−	2.19493i	−0.885116	+	2.68637i	−0.649537	+	0.375010i	−3.84990	−	1.48391i
3.9	0.187641	+	1.40171i	0.198087	−	0.0530773i	−1.92958	+	0.526037i	−0.487744	+	1.82029i	0.111568	+	0.267701i	1.84933	+	1.89208i	−1.09942	−	2.60601i	−2.56165	+	1.47897i	−2.64303	−	0.342115i
3.10	0.438321	−	1.34457i	2.29647	−	0.615336i	−1.61575	−	1.17871i	−0.223959	+	0.835825i	0.179226	−	3.35748i	−1.25761	+	2.32775i	−2.29308	+	1.65584i	2.29704	−	1.32620i	1.02566	+	0.667489i
3.11	0.898888	+	1.09179i	1.30734	−	0.350301i	−0.384000	+	1.96279i	0.294400	−	1.09872i	1.55761	+	1.11246i	−1.56831	−	2.13082i	−2.48812	+	1.34508i	−1.01165	+	0.584076i	1.46420	−	0.666200i
3.12	1.06970	−	0.925063i	−0.246909	+	0.0661591i	0.288515	−	1.97908i	−0.133797	+	0.499339i	−0.202917	+	0.299177i	2.45011	−	0.998472i	−1.52215	−	2.38392i	−2.54149	+	1.46733i	0.318797	+	0.657913i
3.13	1.31418	+	0.522432i	−2.48480	+	0.665801i	1.45413	+	1.37314i	−0.837076	+	3.12401i	−3.61331	−	0.423158i	1.56215	−	2.13534i	1.19362	+	2.56423i	3.13287	−	1.80877i	−2.73215	+	3.66819i
3.14	1.41041	+	0.103712i	−0.885661	+	0.237312i	1.97849	+	0.292553i	0.818796	−	3.05579i	−1.27375	+	0.242853i	−0.640837	+	2.56697i	2.76013	+	0.617811i	−1.87000	+	1.07964i	1.47176	−	4.22498i
19.1	−1.38359	+	0.292689i	0.615336	−	2.29647i	1.82867	−	0.809925i	−0.835825	+	0.223959i	−0.179226	+	3.35748i	−1.25761	−	2.32775i	−2.29308	+	1.65584i	−2.29704	−	1.32620i	1.09089	−	0.554505i
19.2	−1.33598	−	0.463855i	−0.0661591	+	0.246909i	1.56968	+	1.23940i	−0.499339	+	0.133797i	0.202917	−	0.299177i	2.45011	+	0.998472i	−1.52215	−	2.38392i	2.54149	+	1.46733i	0.729168	+	0.0528705i
19.3	−1.29274	+	0.573436i	−0.388227	+	1.44888i	1.34234	−	1.48261i	2.81809	−	0.755106i	−0.328966	−	2.09565i	−1.47726	+	2.19493i	−0.885116	+	2.68637i	0.649537	+	0.375010i	−3.21005	+	2.59215i
19.4	−0.615385	−	1.27330i	−0.237312	+	0.885661i	−1.24260	+	1.56714i	3.05579	−	0.818796i	1.27375	−	0.242853i	−0.640837	−	2.56697i	2.76013	+	0.617811i	1.87000	+	1.07964i	−2.92306	−	3.38707i
19.5	−0.610438	+	1.27568i	−0.204601	+	0.763582i	−1.25473	−	1.55745i	−3.81370	+	1.02188i	−0.849192	−	0.727125i	−2.64575	−	0.00379639i	2.75275	−	0.649913i	2.05688	+	1.18754i	1.02443	−	5.48886i
19.6	−0.482479	+	1.32937i	0.449868	−	1.67893i	−1.53443	−	1.28278i	0.731029	−	0.195879i	2.01486	+	1.40809i	2.52163	+	0.800849i	2.44562	−	1.42090i	−0.0183525	−	0.0105958i	−0.0923119	+	1.06631i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
16.f	odd	4	1	inner
112.v	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	112.2.v.a	✓	56
4.b	odd	2	1		448.2.z.a		56
7.b	odd	2	1		784.2.w.f		56
7.c	even	3	1		784.2.j.a		56
7.c	even	3	1		784.2.w.f		56
7.d	odd	6	1	inner	112.2.v.a	✓	56
7.d	odd	6	1		784.2.j.a		56
8.b	even	2	1		896.2.z.b		56
8.d	odd	2	1		896.2.z.a		56
16.e	even	4	1		448.2.z.a		56
16.e	even	4	1		896.2.z.a		56
16.f	odd	4	1	inner	112.2.v.a	✓	56
16.f	odd	4	1		896.2.z.b		56
28.f	even	6	1		448.2.z.a		56
56.j	odd	6	1		896.2.z.b		56
56.m	even	6	1		896.2.z.a		56
112.j	even	4	1		784.2.w.f		56
112.u	odd	12	1		784.2.j.a		56
112.u	odd	12	1		784.2.w.f		56
112.v	even	12	1	inner	112.2.v.a	✓	56
112.v	even	12	1		784.2.j.a		56
112.v	even	12	1		896.2.z.b		56
112.x	odd	12	1		448.2.z.a		56
112.x	odd	12	1		896.2.z.a		56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
112.2.v.a	✓	56	1.a	even	1	1	trivial
112.2.v.a	✓	56	7.d	odd	6	1	inner
112.2.v.a	✓	56	16.f	odd	4	1	inner
112.2.v.a	✓	56	112.v	even	12	1	inner
448.2.z.a		56	4.b	odd	2	1
448.2.z.a		56	16.e	even	4	1
448.2.z.a		56	28.f	even	6	1
448.2.z.a		56	112.x	odd	12	1
784.2.j.a		56	7.c	even	3	1
784.2.j.a		56	7.d	odd	6	1
784.2.j.a		56	112.u	odd	12	1
784.2.j.a		56	112.v	even	12	1
784.2.w.f		56	7.b	odd	2	1
784.2.w.f		56	7.c	even	3	1
784.2.w.f		56	112.j	even	4	1
784.2.w.f		56	112.u	odd	12	1
896.2.z.a		56	8.d	odd	2	1
896.2.z.a		56	16.e	even	4	1
896.2.z.a		56	56.m	even	6	1
896.2.z.a		56	112.x	odd	12	1
896.2.z.b		56	8.b	even	2	1
896.2.z.b		56	16.f	odd	4	1
896.2.z.b		56	56.j	odd	6	1
896.2.z.b		56	112.v	even	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(112, [\chi])\).