Newform orbit 220.3.n.a

• Label: 220.3.n.a
• Level: $220$
• Weight: $3$
• Character orbit: 220.n
• Analytic conductor: $5.995$
• Analytic rank: $0$
• Dimension: $272$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.n (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.99456581593\)
Analytic rank:	\(0\)
Dimension:	\(272\)
Relative dimension:	\(68\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 272 q - 6 q^{4} - 6 q^{5} + 10 q^{6} - 192 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
59.1	−1.99980	−	0.0280452i	−0.322500	+	0.992552i	3.99843	+	0.112170i	1.92550	+	4.61438i	0.672772	−	1.97586i	0.786438	+	2.42041i	−7.99292	−	0.336454i	6.40000	+	4.64987i	−3.72120	−	9.28185i
59.2	−1.99168	−	0.182208i	1.74937	−	5.38400i	3.93360	+	0.725801i	0.976283	−	4.90376i	−4.46519	+	10.4045i	−1.06057	−	3.26411i	−7.70224	−	2.16230i	−18.6460	−	13.5471i	−2.83795	+	9.58885i
59.3	−1.98733	+	0.224748i	1.18555	−	3.64876i	3.89898	−	0.893297i	−0.255765	+	4.99345i	−1.53604	+	7.51775i	−3.38642	−	10.4223i	−7.54780	+	2.65156i	−4.62675	−	3.36153i	−0.613977	−	9.98113i
59.4	−1.98211	−	0.266910i	−1.39459	+	4.29210i	3.85752	+	1.05809i	4.36346	−	2.44136i	3.90983	−	8.13518i	−2.25420	−	6.93772i	−7.36361	−	3.12686i	−9.19606	−	6.68133i	−9.30048	+	3.67439i
59.5	−1.96450	+	0.375154i	0.297638	−	0.916036i	3.71852	−	1.47398i	2.59881	−	4.27156i	−0.241055	+	1.91121i	3.56529	+	10.9728i	−6.75206	+	4.29066i	6.53062	+	4.74477i	−3.50287	+	9.36643i
59.6	−1.95041	+	0.442590i	0.493733	−	1.51955i	3.60823	−	1.72647i	−4.95116	−	0.697179i	−0.290445	+	3.18228i	1.02359	+	3.15030i	−6.27342	+	4.96429i	5.21588	+	3.78956i	9.96537	−	0.831544i
59.7	−1.94544	+	0.463981i	−1.69177	+	5.20673i	3.56944	−	1.80529i	−3.49424	+	3.57635i	0.875406	−	10.9143i	0.724872	+	2.23093i	−6.10650	+	5.16823i	−16.9668	−	12.3271i	5.13846	−	8.57883i
59.8	−1.86310	−	0.727225i	−0.746523	+	2.29756i	2.94229	+	2.70979i	−4.97494	+	0.499944i	3.06169	−	3.73770i	−2.37053	−	7.29575i	−3.51115	−	7.18831i	2.55966	+	1.85970i	9.63239	+	2.68646i
59.9	−1.81509	−	0.839903i	−1.18739	+	3.65441i	2.58913	+	3.04900i	−2.20769	−	4.48621i	5.22457	−	5.63580i	3.39360	+	10.4444i	−2.13864	−	7.70884i	−4.66365	−	3.38834i	0.239176	+	9.99714i
59.10	−1.81449	+	0.841212i	−0.331631	+	1.02066i	2.58473	−	3.05274i	−2.69892	−	4.20902i	−0.256847	−	2.13094i	−2.85876	−	8.79837i	−2.12195	+	7.71345i	6.34940	+	4.61311i	8.43783	+	5.36684i
59.11	−1.80603	−	0.859222i	0.423044	−	1.30200i	2.52348	+	3.10356i	4.95627	+	0.659848i	−1.88273	+	1.98795i	−0.668808	−	2.05838i	−1.89083	−	7.77334i	5.76493	+	4.18846i	−8.38421	−	5.45024i
59.12	−1.80498	−	0.861422i	1.13599	−	3.49622i	2.51590	+	3.10970i	−4.99633	−	0.191667i	−5.06217	+	5.33204i	1.62081	+	4.98833i	−1.86239	−	7.78020i	−3.65195	−	2.65329i	8.85316	+	4.64990i
59.13	−1.71513	+	1.02875i	−0.881019	+	2.71150i	1.88336	−	3.52888i	4.41135	+	2.35372i	−1.27838	−	5.55693i	−0.513208	−	1.57949i	0.400111	+	7.98999i	0.705121	+	0.512300i	−9.98743	+	0.501225i
59.14	−1.63579	+	1.15074i	1.53627	−	4.72815i	1.35160	−	3.76473i	2.03822	+	4.56570i	2.92786	+	9.50209i	3.85918	+	11.8773i	2.12129	+	7.71363i	−12.7141	−	9.23736i	−8.58803	−	5.12306i
59.15	−1.52786	+	1.29060i	0.813130	−	2.50256i	0.668688	−	3.94371i	4.64314	−	1.85505i	1.98746	+	4.87298i	−1.93951	−	5.96920i	4.06811	+	6.88843i	1.67954	+	1.22026i	−4.69991	+	8.82671i
59.16	−1.37703	−	1.45044i	1.13599	−	3.49622i	−0.207574	+	3.99461i	−1.36166	+	4.81102i	−6.63537	+	3.16671i	1.62081	+	4.98833i	6.07979	−	5.19963i	−3.65195	−	2.65329i	8.85316	−	4.64990i
59.17	−1.37526	−	1.45212i	0.423044	−	1.30200i	−0.217310	+	3.99409i	0.904019	−	4.91760i	−2.47245	+	1.17627i	−0.668808	−	2.05838i	6.09876	−	5.17736i	5.76493	+	4.18846i	−8.38421	+	5.45024i
59.18	−1.36729	+	1.45963i	−1.35989	+	4.18531i	−0.261032	−	3.99147i	−1.91549	−	4.61854i	−4.24964	−	7.70748i	0.119211	+	0.366892i	6.18298	+	5.07650i	−8.38640	−	6.09308i	9.36038	+	3.51899i
59.19	−1.35969	−	1.46671i	−1.18739	+	3.65441i	−0.302489	+	3.98855i	3.58443	+	3.48595i	6.97444	−	3.22730i	3.39360	+	10.4444i	6.26134	−	4.97952i	−4.66365	−	3.38834i	0.239176	−	9.99714i
59.20	−1.34289	+	1.48211i	−0.399083	+	1.22825i	−0.393305	−	3.98062i	−3.44013	+	3.62843i	−1.28448	−	2.24089i	2.62793	+	8.08795i	6.42788	+	4.76260i	5.93182	+	4.30972i	−0.758029	−	9.97123i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	220.3.n.a	✓	272
4.b	odd	2	1	inner	220.3.n.a	✓	272
5.b	even	2	1	inner	220.3.n.a	✓	272
11.c	even	5	1	inner	220.3.n.a	✓	272
20.d	odd	2	1	inner	220.3.n.a	✓	272
44.h	odd	10	1	inner	220.3.n.a	✓	272
55.j	even	10	1	inner	220.3.n.a	✓	272
220.n	odd	10	1	inner	220.3.n.a	✓	272

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
220.3.n.a	✓	272	1.a	even	1	1	trivial
220.3.n.a	✓	272	4.b	odd	2	1	inner
220.3.n.a	✓	272	5.b	even	2	1	inner
220.3.n.a	✓	272	11.c	even	5	1	inner
220.3.n.a	✓	272	20.d	odd	2	1	inner
220.3.n.a	✓	272	44.h	odd	10	1	inner
220.3.n.a	✓	272	55.j	even	10	1	inner
220.3.n.a	✓	272	220.n	odd	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(220, [\chi])\).