Newform orbit 165.4.p.a

• Label: 165.4.p.a
• Level: $165$
• Weight: $4$
• Character orbit: 165.p
• Analytic conductor: $9.735$
• Analytic rank: $0$
• Dimension: $192$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.73531515095\)
Analytic rank:	\(0\)
Dimension:	\(192\)
Relative dimension:	\(48\) 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.

\(\operatorname{Tr}(f)(q) = \) 192 * q + 4 * q^3 - 192 * q^4 - 100 * q^6 + 108 * q^9 + 48 * q^12 - 60 * q^15 - 1248 * q^16 - 460 * q^18 + 900 * q^19 + 888 * q^22 + 1200 * q^24 + 1200 * q^25 + 568 * q^27 - 1680 * q^28 - 576 * q^31 - 1402 * q^33 + 264 * q^34 - 2364 * q^36 + 24 * q^37 + 1220 * q^39 + 4438 * q^42 - 360 * q^46 + 1946 * q^48 + 1848 * q^49 + 930 * q^51 + 840 * q^55 - 4170 * q^57 + 4320 * q^58 - 830 * q^60 - 1560 * q^61 - 7900 * q^63 - 11700 * q^64 - 4214 * q^66 + 168 * q^67 - 4992 * q^69 - 1620 * q^70 + 6720 * q^72 - 360 * q^73 + 150 * q^75 + 13972 * q^78 + 4740 * q^79 + 916 * q^81 + 6420 * q^82 + 6880 * q^84 + 2868 * q^88 + 8736 * q^91 - 5696 * q^93 - 840 * q^94 - 12470 * q^96 - 7356 * q^97 - 736 * q^99

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
41.1	−4.37775	+	3.18062i	5.19597	+	0.0430816i	6.57619	−	20.2394i	2.93893	−	4.04508i	−22.8837	+	16.3378i	−17.6902	−	5.74790i	22.2078	+	68.3486i	26.9963	+	0.447702i			27.0560i
41.2	−4.33342	+	3.14842i	1.85440	+	4.85399i	6.39390	−	19.6784i	−2.93893	+	4.04508i	−23.3183	−	15.1960i	16.5829	+	5.38812i	21.0066	+	64.6515i	−20.1224	+	18.0025i		−	26.7820i
41.3	−4.31401	+	3.13431i	−4.16964	−	3.10066i	6.31465	−	19.4345i	2.93893	−	4.04508i	27.7063	+	0.307340i	6.06872	+	1.97185i	20.4899	+	63.0614i	7.77178	+	25.8573i			26.6621i
41.4	−4.12943	+	3.00021i	1.71341	−	4.90553i	5.57881	−	17.1698i	−2.93893	+	4.04508i	7.64218	+	25.3976i	−24.5008	−	7.96079i	15.8573	+	48.8036i	−21.1284	−	16.8104i		−	25.5213i
41.5	−3.95634	+	2.87445i	−3.12055	+	4.15478i	4.91804	−	15.1362i	2.93893	−	4.04508i	0.403271	−	25.4076i	12.3288	+	4.00588i	11.9612	+	36.8128i	−7.52432	−	25.9304i			24.4515i
41.6	−3.94368	+	2.86525i	−4.41355	+	2.74237i	4.87081	−	14.9908i	−2.93893	+	4.04508i	9.54802	−	23.4610i	−18.8401	−	6.12152i	11.6927	+	35.9864i	11.9588	−	24.2072i		−	24.3733i
41.7	−3.55039	+	2.57951i	−3.58250	−	3.76374i	3.47925	−	10.7080i	−2.93893	+	4.04508i	22.4278	+	4.12164i	8.73323	+	2.83760i	4.41974	+	13.6026i	−1.33143	+	26.9672i		−	21.9426i
41.8	−3.32358	+	2.41473i	4.15843	+	3.11568i	2.74318	−	8.44263i	2.93893	−	4.04508i	−21.3444	−	0.313780i	11.3617	+	3.69163i	1.11348	+	3.42695i	7.58503	+	25.9127i			20.5409i
41.9	−3.12619	+	2.27131i	5.16730	−	0.546811i	2.14208	−	6.59266i	−2.93893	+	4.04508i	−14.9120	+	13.4460i	16.5110	+	5.36474i	−1.27538	−	3.92522i	26.4020	−	5.65107i		−	19.3209i
41.10	−2.84801	+	2.06920i	4.14644	−	3.13162i	1.35744	−	4.17778i	2.93893	−	4.04508i	−5.32916	+	17.4987i	−7.01306	−	2.27868i	−3.92409	−	12.0771i	7.38594	−	25.9701i			17.6017i
41.11	−2.81316	+	2.04388i	−1.01719	−	5.09562i	1.26428	−	3.89106i	2.93893	−	4.04508i	13.2763	+	12.2558i	−23.9271	−	7.77440i	−4.20002	−	12.9263i	−24.9307	+	10.3664i			17.3863i
41.12	−2.44441	+	1.77597i	5.06426	+	1.16331i	0.348949	−	1.07396i	−2.93893	+	4.04508i	−14.4451	+	6.15036i	−25.0543	−	8.14063i	−6.41512	−	19.7437i	24.2934	+	11.7826i		−	15.1073i
41.13	−2.41966	+	1.75799i	−5.15998	+	0.612021i	0.292106	−	0.899011i	−2.93893	+	4.04508i	11.4095	−	10.5521i	29.5600	+	9.60462i	−6.52018	−	20.0670i	26.2509	−	6.31604i		−	14.9543i
41.14	−2.41426	+	1.75406i	−1.09514	+	5.07944i	0.279774	−	0.861056i	2.93893	−	4.04508i	−6.26568	−	14.1840i	9.59193	+	3.11661i	−6.54242	−	20.1355i	−24.6013	−	11.1254i			14.9209i
41.15	−2.06223	+	1.49830i	−1.66099	+	4.92353i	−0.464244	+	1.42880i	−2.93893	+	4.04508i	−3.95157	−	12.6421i	−1.91226	−	0.621330i	−7.48499	−	23.0364i	−21.4822	−	16.3558i		−	12.7453i
41.16	−1.85179	+	1.34540i	−0.851496	−	5.12591i	−0.853127	+	2.62565i	2.93893	−	4.04508i	8.47320	+	8.34649i	28.0892	+	9.12673i	−7.61131	−	23.4252i	−25.5499	+	8.72938i			11.4447i
41.17	−1.78814	+	1.29916i	2.75584	−	4.40515i	−0.962500	+	2.96227i	−2.93893	+	4.04508i	0.795157	+	11.4573i	−4.06416	−	1.32053i	−7.59147	−	23.3641i	−11.8106	−	24.2798i		−	11.0513i
41.18	−1.35979	+	0.987942i	−5.19037	+	0.245075i	−1.59915	+	4.92167i	2.93893	−	4.04508i	6.81567	−	5.46103i	18.3598	+	5.96546i	−6.84296	−	21.0605i	26.8799	−	2.54406i			8.40394i
41.19	−1.01327	+	0.736186i	3.14372	+	4.13727i	−1.98738	+	6.11654i	−2.93893	+	4.04508i	−6.23125	−	1.87782i	29.0946	+	9.45342i	−5.58543	−	17.1902i	−7.23403	+	26.0129i		−	6.26237i
41.20	−0.923458	+	0.670932i	2.66996	+	4.45772i	−2.06951	+	6.36930i	2.93893	−	4.04508i	−5.45643	−	2.32516i	−17.6104	−	5.72198i	−5.18409	−	15.9550i	−12.7426	+	23.8039i			5.70729i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
11.d	odd	10	1	inner
33.f	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	165.4.p.a	✓	192
3.b	odd	2	1	inner	165.4.p.a	✓	192
11.d	odd	10	1	inner	165.4.p.a	✓	192
33.f	even	10	1	inner	165.4.p.a	✓	192

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
165.4.p.a	✓	192	1.a	even	1	1	trivial
165.4.p.a	✓	192	3.b	odd	2	1	inner
165.4.p.a	✓	192	11.d	odd	10	1	inner
165.4.p.a	✓	192	33.f	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(165, [\chi])\).