Newform orbit 79.4.g.a

• Label: 79.4.g.a
• Level: $79$
• Weight: $4$
• Character orbit: 79.g
• Analytic conductor: $4.661$
• Analytic rank: $0$
• Dimension: $456$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	79.g (of order \(39\), degree \(24\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.66115089045\)
Analytic rank:	\(0\)
Dimension:	\(456\)
Relative dimension:	\(19\) over \(\Q(\zeta_{39})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 456 q - 26 q^{2} - 19 q^{3} + 64 q^{4} - 25 q^{5} - 41 q^{6} - 43 q^{7} - 58 q^{8} + 112 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−4.24677	−	3.19124i	−0.944542	−	0.153503i	5.62532	+	19.4208i	2.83152	+	1.79054i	3.52139	+	3.66616i	20.6668	−	25.3122i	23.0174	−	60.6920i	−24.7419	−	8.26006i	−6.31076	−	16.6401i
2.2	−3.91681	−	2.94329i	−6.66109	−	1.08253i	4.45270	+	15.3725i	−13.7056	−	8.66687i	22.9040	+	23.8456i	−16.3404	+	20.0133i	13.9065	−	36.6685i	17.5877	+	5.87165i	28.1730	+	74.2860i
2.3	−3.61319	−	2.71514i	10.1077	+	1.64266i	3.45745	+	11.9365i	−11.0352	−	6.97821i	−32.0610	−	33.3791i	8.54192	−	10.4620i	7.09533	−	18.7089i	73.8569	+	24.6570i	20.9254	+	55.1756i
2.4	−3.38295	−	2.54212i	2.87624	+	0.467434i	2.75621	+	9.51556i	1.09240	+	0.690791i	−8.54188	−	8.89304i	−12.9938	+	15.9145i	2.86110	−	7.54410i	−17.5562	−	5.86113i	−1.93945	−	5.11391i
2.5	−2.97647	−	2.23667i	−6.54416	−	1.06353i	1.63094	+	5.63066i	16.1077	+	10.1859i	17.0997	+	17.8027i	−0.273516	+	0.334996i	−2.82258	+	7.44252i	16.0844	+	5.36976i	−25.1615	−	66.3456i
2.6	−2.09643	−	1.57536i	1.35214	+	0.219744i	−0.312504	−	1.07889i	−2.75938	−	1.74493i	−2.48848	−	2.59078i	8.11742	−	9.94204i	−8.48371	+	22.3697i	−23.8305	−	7.95579i	3.03594	+	8.00513i
2.7	−1.62506	−	1.22115i	7.00466	+	1.13837i	−1.07613	−	3.71524i	14.4602	+	9.14410i	−9.99289	−	10.4037i	2.01901	−	2.47284i	−8.55467	+	22.5568i	22.1589	+	7.39774i	−12.3324	−	32.5179i
2.8	−1.54245	−	1.15908i	−7.12903	−	1.15858i	−1.19004	−	4.10851i	−6.98627	−	4.41785i	9.65330	+	10.0501i	7.27312	−	8.90795i	−8.39991	+	22.1487i	23.8703	+	7.96909i	5.65535	+	14.9119i
2.9	−0.650255	−	0.488635i	4.07726	+	0.662619i	−2.04167	−	7.04867i	−15.4326	−	9.75896i	−2.32748	−	2.42316i	−15.7864	+	19.3348i	−4.42406	+	11.6653i	−9.42552	−	3.14670i	5.26653	+	13.8867i
2.10	0.194813	+	0.146392i	−4.71146	−	0.765687i	−2.20922	−	7.62711i	7.97193	+	5.04114i	−0.805763	−	0.838888i	−19.2237	+	23.5447i	1.37746	−	3.63207i	−3.99888	−	1.33502i	0.815049	+	2.14911i
2.11	0.437267	+	0.328585i	−0.306228	−	0.0497668i	−2.14251	−	7.39679i	2.62240	+	1.65831i	−0.117551	−	0.122383i	6.93592	−	8.49496i	3.04527	−	8.02973i	−25.5192	−	8.51956i	0.601795	+	1.58680i
2.12	0.888431	+	0.667613i	7.22480	+	1.17414i	−1.88214	−	6.49789i	−7.88897	−	4.98868i	5.63486	+	5.86651i	21.6990	−	26.5764i	5.81854	−	15.3422i	25.2086	+	8.41586i	−3.67830	−	9.69888i
2.13	1.76028	+	1.32276i	8.51679	+	1.38411i	−0.876864	−	3.02729i	4.07882	+	2.57929i	13.1611	+	13.7021i	−14.7453	+	18.0597i	8.70724	−	22.9591i	45.0094	+	15.0263i	3.76807	+	9.93559i
2.14	2.17097	+	1.63138i	−9.23258	−	1.50044i	−0.174017	−	0.600778i	10.9083	+	6.89800i	−17.5959	−	18.3193i	16.8765	−	20.6699i	8.30605	−	21.9013i	57.3788	+	19.1558i	12.4284	+	32.7710i
2.15	2.34214	+	1.76001i	−4.13705	−	0.672335i	0.162276	+	0.560240i	−13.0107	−	8.22749i	−8.50624	−	8.85594i	1.08786	−	1.33239i	7.70519	−	20.3169i	−8.94738	−	2.98707i	−15.9926	−	42.1690i
2.16	2.36936	+	1.78046i	2.94647	+	0.478848i	0.218094	+	0.752949i	12.0257	+	7.60456i	6.12868	+	6.38064i	−2.12499	+	2.60264i	7.58387	−	19.9970i	−17.1581	−	5.72821i	14.9535	+	39.4291i
2.17	3.79491	+	2.85169i	6.47301	+	1.05197i	4.04347	+	13.9597i	−10.5397	−	6.66493i	21.5646	+	22.4511i	−2.06310	+	2.52684i	−10.9978	+	28.9987i	15.1827	+	5.06873i	−20.9911	−	55.3489i
2.18	3.80779	+	2.86137i	0.469501	+	0.0763013i	4.08609	+	14.1068i	6.99646	+	4.42429i	1.56943	+	1.63395i	7.55497	−	9.25315i	−11.2938	+	29.7793i	−25.3959	−	8.47839i	13.9815	+	36.8662i
2.19	3.99500	+	3.00205i	−7.40866	−	1.20402i	4.72200	+	16.3022i	0.834290	+	0.527573i	−25.9831	−	27.0513i	−21.5539	+	26.3988i	−15.8994	+	41.9232i	27.8281	+	9.29039i	1.74919	+	4.61223i
4.1	−1.52345	−	5.25958i	1.63359	+	0.545372i	−18.5807	+	11.7497i	−8.41811	−	17.7408i	0.379727	−	9.42284i	3.78167	+	18.5239i	57.3160	+	50.7776i	−19.2138	−	14.4382i	−80.4844	+	71.3030i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
79.g	even	39	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	79.4.g.a	✓	456
79.g	even	39	1	inner	79.4.g.a	✓	456

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
79.4.g.a	✓	456	1.a	even	1	1	trivial
79.4.g.a	✓	456	79.g	even	39	1	inner

Hecke kernels

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