Newform orbit 220.2.v.a

• Label: 220.2.v.a
• Level: $220$
• Weight: $2$
• Character orbit: 220.v
• Analytic conductor: $1.757$
• Analytic rank: $0$
• Dimension: $256$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.v (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.75670884447\)
Analytic rank:	\(0\)
Dimension:	\(256\)
Relative dimension:	\(32\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 256 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 6 q^{8}+O(q^{10}) \)

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	−1.38961	+	0.262645i	2.82414	+	1.43897i	1.86204	−	0.729949i	−2.14085	+	0.645564i	−4.30240	−	1.25786i	2.11465	−	1.07747i	−2.39579	+	1.50340i	4.14178	+	5.70067i	2.80540	−	1.45937i
3.2	−1.38610	+	0.280565i	−0.481605	−	0.245390i	1.84257	−	0.777784i	1.65529	−	1.50333i	0.736402	+	0.205014i	−0.559468	+	0.285063i	−2.33577	+	1.59505i	−1.59163	−	2.19069i	−1.87263	+	2.54819i
3.3	−1.36366	−	0.374731i	−0.0905018	−	0.0461129i	1.71915	+	1.02201i	−1.28673	+	1.82875i	0.106134	+	0.0967963i	−2.47893	+	1.26308i	−1.96137	−	2.03790i	−1.75729	−	2.41870i	2.43996	−	2.01162i
3.4	−1.35127	−	0.417227i	−2.00530	−	1.02175i	1.65184	+	1.12757i	−1.34468	−	1.78657i	2.28340	+	2.21733i	3.86673	−	1.97020i	−1.76163	−	2.21284i	1.21390	+	1.67079i	1.07162	+	2.97517i
3.5	−1.31645	+	0.516682i	0.249901	+	0.127331i	1.46608	−	1.36037i	1.01317	+	1.99336i	−0.394772	−	0.0385054i	3.32120	−	1.69223i	−1.22714	+	2.54836i	−1.71712	−	2.36341i	−2.36372	−	2.10067i
3.6	−1.21176	+	0.729133i	−2.01401	−	1.02619i	0.936729	−	1.76707i	−2.19782	−	0.411812i	3.18873	−	0.224986i	−1.87240	+	0.954035i	0.153338	+	2.82427i	1.23982	+	1.70646i	2.96350	−	1.10349i
3.7	−1.17385	−	0.788721i	1.93820	+	0.987564i	0.755839	+	1.85168i	1.94109	+	1.11003i	−1.49624	−	2.68795i	−0.647272	+	0.329802i	0.573215	−	2.76973i	1.01800	+	1.40115i	−1.40305	−	2.83398i
3.8	−1.05295	−	0.944087i	1.34150	+	0.683529i	0.217399	+	1.98815i	−0.948637	−	2.02487i	−0.767221	−	1.98622i	0.566907	−	0.288854i	1.64808	−	2.29866i	−0.430940	−	0.593138i	−0.912785	+	3.02768i
3.9	−0.986606	+	1.01322i	2.54367	+	1.29607i	−0.0532170	−	1.99929i	2.18490	−	0.475619i	−3.82280	+	1.29859i	−2.92618	+	1.49096i	2.07822	+	1.91859i	3.02712	+	4.16648i	−1.67373	+	2.68303i
3.10	−0.798140	−	1.16746i	−2.10822	−	1.07419i	−0.725945	+	1.86360i	−0.446641	+	2.19101i	0.428575	+	3.31863i	0.857802	−	0.437072i	2.75509	−	0.639900i	1.52735	+	2.10222i	2.91440	−	1.22729i
3.11	−0.747186	+	1.20071i	−1.63676	−	0.833969i	−0.883427	−	1.79431i	1.66521	+	1.49234i	2.22432	−	1.34215i	−2.18680	+	1.11423i	2.81454	+	0.279941i	0.220109	+	0.302954i	−3.03609	+	0.884393i
3.12	−0.557475	+	1.29970i	0.996151	+	0.507564i	−1.37844	−	1.44910i	0.0455245	−	2.23560i	−1.21501	+	1.01174i	3.44949	−	1.75760i	2.65185	−	0.983725i	−1.02866	−	1.41583i	2.88024	+	1.30546i
3.13	−0.544739	−	1.30509i	−0.771035	−	0.392862i	−1.40652	+	1.42187i	2.10061	−	0.766443i	−0.0927074	+	1.22028i	1.98436	−	1.01108i	2.62185	+	1.06109i	−1.32320	−	1.82123i	−2.14456	−	2.32397i
3.14	−0.268903	−	1.38841i	0.131087	+	0.0667921i	−1.85538	+	0.746697i	−2.22160	−	0.253930i	0.0574854	−	0.199963i	−2.72311	+	1.38749i	1.53564	+	2.37525i	−1.75063	−	2.40954i	0.244837	+	3.15279i
3.15	−0.262448	+	1.38965i	−1.70123	−	0.866818i	−1.86224	−	0.729420i	−1.70162	+	1.45068i	1.65105	−	2.13661i	3.08760	−	1.57321i	1.50238	−	2.39643i	0.379441	+	0.522256i	−1.56935	−	2.74538i
3.16	−0.179822	+	1.40273i	1.70123	+	0.866818i	−1.93533	−	0.504485i	−1.70162	+	1.45068i	−1.52183	+	2.23050i	−3.08760	+	1.57321i	1.05567	−	2.62403i	0.379441	+	0.522256i	−1.72894	−	2.64779i
3.17	0.128561	+	1.40836i	−0.996151	−	0.507564i	−1.96694	+	0.362119i	0.0455245	−	2.23560i	0.586766	−	1.46819i	−3.44949	+	1.75760i	−0.762865	−	2.72361i	−1.02866	−	1.41583i	3.15438	−	0.223296i
3.18	0.165017	−	1.40455i	2.76215	+	1.40739i	−1.94554	−	0.463549i	0.373763	−	2.20461i	2.43255	−	3.64734i	1.22421	−	0.623768i	−0.972126	+	2.65612i	3.88538	+	5.34777i	−3.03481	−	0.888767i
3.19	0.277091	−	1.38680i	−2.76215	−	1.40739i	−1.84644	−	0.768540i	0.373763	−	2.20461i	−2.71713	+	3.44058i	−1.22421	+	0.623768i	−1.57744	+	2.34769i	3.88538	+	5.34777i	−2.95379	−	1.12921i
3.20	0.339575	+	1.37284i	1.63676	+	0.833969i	−1.76938	+	0.932363i	1.66521	+	1.49234i	−0.589104	+	2.53020i	2.18680	−	1.11423i	−1.88082	−	2.11247i	0.220109	+	0.302954i	−1.48327	+	2.79283i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.c	odd	4	1	inner
11.c	even	5	1	inner
20.e	even	4	1	inner
44.h	odd	10	1	inner
55.k	odd	20	1	inner
220.v	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	220.2.v.a	✓	256
4.b	odd	2	1	inner	220.2.v.a	✓	256
5.c	odd	4	1	inner	220.2.v.a	✓	256
11.c	even	5	1	inner	220.2.v.a	✓	256
20.e	even	4	1	inner	220.2.v.a	✓	256
44.h	odd	10	1	inner	220.2.v.a	✓	256
55.k	odd	20	1	inner	220.2.v.a	✓	256
220.v	even	20	1	inner	220.2.v.a	✓	256

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
220.2.v.a	✓	256	1.a	even	1	1	trivial
220.2.v.a	✓	256	4.b	odd	2	1	inner
220.2.v.a	✓	256	5.c	odd	4	1	inner
220.2.v.a	✓	256	11.c	even	5	1	inner
220.2.v.a	✓	256	20.e	even	4	1	inner
220.2.v.a	✓	256	44.h	odd	10	1	inner
220.2.v.a	✓	256	55.k	odd	20	1	inner
220.2.v.a	✓	256	220.v	even	20	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(220, [\chi])\).