Newform orbit 176.3.k.a

• Label: 176.3.k.a
• Level: $176$
• Weight: $3$
• Character orbit: 176.k
• Analytic conductor: $4.796$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	176.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.79565265274\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(40\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q + 12 q^{6} - 12 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
67.1	−1.99851	−	0.0770689i	1.07248	−	1.07248i	3.98812	+	0.308047i	−0.304086	+	0.304086i	−2.22603	+	2.06072i	−11.6207			−7.94658	−	0.922996i			6.69955i	0.631157	−	0.584285i
67.2	−1.99789	+	0.0918875i	−4.17245	+	4.17245i	3.98311	−	0.367162i	2.54514	−	2.54514i	7.95270	−	8.71949i	−8.66712			−7.92408	+	1.09955i		−	25.8187i	−4.85103	+	5.31877i
67.3	−1.98372	−	0.254671i	0.496048	−	0.496048i	3.87029	+	1.01039i	6.19535	−	6.19535i	−1.11035	+	0.857691i	6.04640			−7.42024	−	2.98998i			8.50787i	−13.8676	+	10.7121i
67.4	−1.97373	−	0.323076i	−2.45130	+	2.45130i	3.79124	+	1.27533i	−1.68733	+	1.68733i	5.63017	−	4.04625i	12.4055			−7.07087	−	3.74203i		−	3.01774i	3.87547	−	2.78520i
67.5	−1.94949	+	0.446643i	1.62128	−	1.62128i	3.60102	−	1.74145i	−3.07749	+	3.07749i	−2.43653	+	3.88480i	6.13719			−6.24234	+	5.00332i			3.74292i	4.62500	−	7.37408i
67.6	−1.83674	−	0.791445i	4.13044	−	4.13044i	2.74723	+	2.90736i	2.66857	−	2.66857i	−10.8556	+	4.31753i	−2.83094			−2.74493	−	7.51434i		−	25.1211i	−7.01350	+	2.78944i
67.7	−1.71503	+	1.02891i	−1.98641	+	1.98641i	1.88268	−	3.52924i	−4.28548	+	4.28548i	1.36292	−	5.45060i	−1.79479			0.402412	+	7.98987i			1.10837i	2.94036	−	11.7591i
67.8	−1.59058	+	1.21246i	2.90002	−	2.90002i	1.05991	−	3.85702i	3.66820	−	3.66820i	−1.09658	+	8.12887i	2.50062			2.99060	+	7.42000i		−	7.82027i	−1.38705	+	10.2821i
67.9	−1.55544	+	1.25723i	−1.44242	+	1.44242i	0.838764	−	3.91107i	1.90168	−	1.90168i	0.430145	−	4.05704i	−1.15133			3.61246	+	7.13794i			4.83884i	−0.567101	+	5.34879i
67.10	−1.54150	−	1.27428i	−1.94599	+	1.94599i	0.752437	+	3.92859i	−0.736537	+	0.736537i	5.47948	−	0.520013i	1.14749			3.84623	−	7.01473i			1.42621i	2.07392	−	0.196819i
67.11	−1.53159	−	1.28617i	−1.33764	+	1.33764i	0.691542	+	3.93977i	3.71371	−	3.71371i	3.76916	−	0.328288i	−5.35963			4.00804	−	6.92355i			5.42142i	−10.4643	+	0.911429i
67.12	−1.19804	+	1.60147i	3.43211	−	3.43211i	−1.12942	−	3.83724i	−6.57313	+	6.57313i	1.38463	+	9.60822i	−10.5496			7.49831	+	2.78842i		−	14.5588i	−2.65183	−	18.4015i
67.13	−0.840357	+	1.81488i	−3.50883	+	3.50883i	−2.58760	−	3.05030i	4.62771	−	4.62771i	−3.41945	−	9.31678i	12.6047			7.71044	−	2.13285i		−	15.6238i	4.50982	+	12.2877i
67.14	−0.823887	−	1.82242i	2.06950	−	2.06950i	−2.64242	+	3.00293i	4.28057	−	4.28057i	−5.47654	−	2.06647i	11.6192			7.64966	+	2.34152i			0.434311i	−11.3277	−	4.27429i
67.15	−0.794054	−	1.83561i	−3.85635	+	3.85635i	−2.73896	+	2.91515i	−5.56053	+	5.56053i	10.1409	+	4.01662i	−3.52698			7.52598	+	2.71288i		−	20.7428i	14.6223	+	5.79162i
67.16	−0.670141	+	1.88439i	1.36978	−	1.36978i	−3.10182	−	2.52561i	−2.05346	+	2.05346i	1.66325	+	3.49914i	6.31785			6.83788	−	4.15252i			5.24741i	−2.49340	−	5.24561i
67.17	−0.633197	−	1.89712i	0.466375	−	0.466375i	−3.19812	+	2.40250i	−1.44097	+	1.44097i	−1.18008	−	0.589461i	−6.06519			6.58287	+	4.54596i			8.56499i	3.64611	+	1.82128i
67.18	−0.383398	+	1.96291i	−2.85242	+	2.85242i	−3.70601	−	1.50515i	−4.98967	+	4.98967i	−4.50543	−	6.69266i	−0.930878			4.37535	−	6.69749i		−	7.27265i	−7.88122	−	11.7073i
67.19	−0.199043	−	1.99007i	3.43093	−	3.43093i	−3.92076	+	0.792220i	0.225895	−	0.225895i	−7.51071	−	6.14490i	−9.36464			2.35697	+	7.64491i		−	14.5426i	−0.494510	−	0.404584i
67.20	−0.0926860	−	1.99785i	−2.65717	+	2.65717i	−3.98282	+	0.370346i	5.90902	−	5.90902i	5.55491	+	5.06235i	−4.39923			1.10905	+	7.92275i		−	5.12110i	−12.3530	−	11.2577i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.f	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	176.3.k.a	✓	80
4.b	odd	2	1		704.3.k.a		80
16.e	even	4	1		704.3.k.a		80
16.f	odd	4	1	inner	176.3.k.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
176.3.k.a	✓	80	1.a	even	1	1	trivial
176.3.k.a	✓	80	16.f	odd	4	1	inner
704.3.k.a		80	4.b	odd	2	1
704.3.k.a		80	16.e	even	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(176, [\chi])\).