Newform orbit 79.4.e.a

• Label: 79.4.e.a
• Level: $79$
• Weight: $4$
• Character orbit: 79.e
• Analytic conductor: $4.661$
• Analytic rank: $0$
• Dimension: $228$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	79.e (of order \(13\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.66115089045\)
Analytic rank:	\(0\)
Dimension:	\(228\)
Relative dimension:	\(19\) over \(\Q(\zeta_{13})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 228 q - 13 q^{2} - 11 q^{3} - 85 q^{4} - 11 q^{5} + 5 q^{6} - 17 q^{7} + 127 q^{8} - 196 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
8.1	−1.97213	+	5.20009i	0.228734	+	0.120049i	−17.1635	−	15.2056i	1.29042	−	10.6276i	−1.07536	+	0.952683i	11.6011	+	6.08875i	73.5233	−	38.5880i	−15.2998	−	22.1656i	52.7195	+	27.6693i
8.2	−1.61939	+	4.26997i	8.28856	+	4.35017i	−9.62213	−	8.52446i	−0.372407	+	3.06705i	−31.9975	+	28.3473i	−27.0594	−	14.2019i	19.6320	−	10.3037i	34.4384	+	49.8927i	−12.4931	−	6.55690i
8.3	−1.61158	+	4.24939i	−8.68380	−	4.55761i	−9.47203	−	8.39148i	−0.285252	+	2.34927i	33.3617	−	29.5559i	−5.41441	−	2.84170i	18.7304	−	9.83047i	39.2988	+	56.9341i	−9.52323	−	4.99818i
8.4	−1.46616	+	3.86595i	−0.920895	−	0.483323i	−6.80785	−	6.03123i	−1.94370	+	16.0078i	3.21868	−	2.85150i	−0.361078	−	0.189508i	4.00953	−	2.10436i	−14.7233	−	21.3304i	−59.0355	−	30.9842i
8.5	−1.22357	+	3.22630i	0.0269131	+	0.0141251i	−2.92380	−	2.59026i	2.01600	−	16.6033i	−0.0785019	+	0.0695466i	−22.3762	−	11.7439i	−12.5079	+	6.56464i	−15.3372	−	22.2198i	51.1004	+	26.8196i
8.6	−1.17201	+	3.09034i	5.84666	+	3.06856i	−2.18849	−	1.93884i	0.358618	−	2.95348i	−16.3352	+	14.4718i	28.3181	+	14.8625i	−14.8557	+	7.79687i	9.42956	+	13.6611i	8.70695	+	4.56976i
8.7	−0.873856	+	2.30417i	−5.35641	−	2.81126i	1.44252	+	1.27796i	1.23306	−	10.1552i	11.1583	−	9.88543i	26.8828	+	14.1092i	−21.6615	+	11.3688i	5.45017	+	7.89593i	22.3217	+	11.7154i
8.8	−0.419844	+	1.10704i	−5.24754	−	2.75412i	4.93882	+	4.37542i	0.144582	−	1.19074i	5.25206	−	4.65292i	−14.8566	−	7.79734i	−15.3042	+	8.03224i	4.61373	+	6.68414i	1.25750	+	0.659984i
8.9	−0.265535	+	0.700158i	1.50580	+	0.790304i	5.56837	+	4.93315i	−1.23482	+	10.1697i	−0.953181	+	0.844444i	−3.32923	−	1.74731i	−10.2370	+	5.37277i	−13.6949	−	19.8405i	−6.79249	−	3.56497i
8.10	−0.224203	+	0.591174i	6.52990	+	3.42715i	5.68887	+	5.03990i	−0.881782	+	7.26213i	−3.49007	+	3.09193i	−6.54263	−	3.43383i	−8.73363	+	4.58376i	15.5564	+	22.5374i	−4.09548	−	2.14947i
8.11	0.176367	−	0.465041i	5.48865	+	2.88066i	5.80293	+	5.14095i	2.31506	−	19.0663i	2.30764	−	2.04439i	−1.20764	−	0.633816i	6.93733	−	3.64099i	6.48927	+	9.40133i	−8.45829	−	4.43925i
8.12	0.554606	−	1.46238i	−7.52478	−	3.94931i	4.15713	+	3.68290i	−1.73243	+	14.2679i	−9.94866	+	8.81374i	−0.549150	−	0.288216i	18.7702	−	9.85139i	25.6875	+	37.2148i	19.9041	+	10.4465i
8.13	0.570719	−	1.50486i	−2.11407	−	1.10955i	4.04919	+	3.58727i	1.05093	−	8.65517i	−2.87626	+	2.54814i	18.1632	+	9.53279i	19.1101	−	10.0298i	−12.0996	−	17.5292i	−12.4251	−	6.52117i
8.14	1.05678	−	2.78650i	1.97550	+	1.03682i	−0.659699	−	0.584442i	−1.96526	+	16.1853i	4.97677	−	4.40903i	25.0185	+	13.1307i	18.7847	−	9.85897i	−12.5102	−	18.1241i	43.0236	+	22.5805i
8.15	1.15913	−	3.05636i	−1.89128	−	0.992621i	−2.00970	−	1.78044i	0.816486	−	6.72436i	−5.22604	+	4.62987i	−23.2713	−	12.2137i	15.3837	−	8.07401i	−12.7461	−	18.4659i	−19.6057	−	10.2899i
8.16	1.20110	−	3.16705i	7.24029	+	3.80000i	−2.59945	−	2.30291i	−0.504284	+	4.15316i	20.7311	−	18.3662i	−9.16214	−	4.80866i	13.5778	−	7.12617i	22.6441	+	32.8057i	12.5475	+	6.58546i
8.17	1.60532	−	4.23289i	−7.64332	−	4.01152i	−9.35218	−	8.28531i	1.13146	−	9.31844i	−29.2503	+	25.9135i	12.5701	+	6.59732i	−18.0158	+	9.45544i	26.9902	+	39.1021i	−37.6275	−	19.7484i
8.18	1.81468	−	4.78493i	3.67907	+	1.93093i	−13.6144	−	12.0613i	1.03316	−	8.50881i	15.9157	−	14.1001i	9.25465	+	4.85722i	−46.1677	+	24.2307i	−5.53066	−	8.01254i	−38.8392	−	20.3844i
8.19	1.83011	−	4.82562i	−2.99605	−	1.57245i	−13.9492	−	12.3579i	−2.49891	+	20.5804i	−13.0712	+	11.5800i	−16.9384	−	8.88995i	−48.6043	+	25.5095i	−8.83402	−	12.7983i	94.7396	+	49.7232i
10.1	−1.97213	−	5.20009i	0.228734	−	0.120049i	−17.1635	+	15.2056i	1.29042	+	10.6276i	−1.07536	−	0.952683i	11.6011	−	6.08875i	73.5233	+	38.5880i	−15.2998	+	22.1656i	52.7195	−	27.6693i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
79.e	even	13	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	79.4.e.a	✓	228
79.e	even	13	1	inner	79.4.e.a	✓	228

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
79.4.e.a	✓	228	1.a	even	1	1	trivial
79.4.e.a	✓	228	79.e	even	13	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(79, [\chi])\).