Newform orbit 79.5.f.a

• Label: 79.5.f.a
• Level: $79$
• Weight: $5$
• Character orbit: 79.f
• Analytic conductor: $8.166$
• Analytic rank: $0$
• Dimension: $300$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	79.f (of order \(26\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.16622708362\)
Analytic rank:	\(0\)
Dimension:	\(300\)
Relative dimension:	\(25\) over \(\Q(\zeta_{26})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 300 q - 17 q^{2} - 13 q^{3} - 221 q^{4} - 11 q^{5} - 13 q^{6} - 13 q^{7} + 459 q^{8} + 624 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
12.1	−0.880563	−	7.25209i	−9.65770	−	3.66268i	−36.2824	+	8.94280i	10.7508	+	5.64246i	−18.0579	+	73.2637i	−10.6557	−	4.04117i	55.3547	+	145.958i	19.2265	+	17.0332i	31.4529	−	82.9344i
12.2	−0.857180	−	7.05952i	6.71608	+	2.54707i	−33.5669	+	8.27351i	33.3680	+	17.5129i	12.2242	−	49.5956i	53.6484	+	20.3461i	46.8323	+	123.487i	−22.0112	−	19.5002i	95.0300	−	250.573i
12.3	−0.837468	−	6.89717i	8.79602	+	3.33589i	−31.3345	+	7.72327i	−21.8137	−	11.4487i	15.6418	−	63.4613i	−13.1124	−	4.97287i	40.0906	+	105.710i	5.61243	+	4.97218i	−60.6953	+	160.040i
12.4	−0.710891	−	5.85472i	−9.91873	−	3.76168i	−18.2373	+	4.49508i	−37.2186	−	19.5338i	−14.9724	+	60.7455i	17.7079	+	6.71570i	5.82039	+	15.3471i	23.6017	+	20.9092i	−87.9066	+	231.791i
12.5	−0.570567	−	4.69905i	−1.80843	−	0.685848i	−6.22041	+	1.53319i	25.7388	+	13.5087i	−2.19100	+	8.88923i	−74.0027	−	28.0655i	−16.1030	−	42.4601i	−57.8293	−	51.2323i	48.7925	−	128.655i
12.6	−0.562063	−	4.62900i	16.5307	+	6.26928i	−5.57667	+	1.37453i	16.3245	+	8.56774i	19.7292	−	80.0446i	−54.0880	−	20.5129i	−16.9592	−	44.7178i	173.332	+	153.559i	30.4847	−	80.3816i
12.7	−0.516103	−	4.25049i	−2.41955	−	0.917613i	−2.26526	+	0.558337i	−2.95535	−	1.55109i	−2.65157	+	10.7578i	−5.92784	−	2.24813i	−20.7507	−	54.7152i	−55.6172	−	49.2725i	−5.06762	+	13.3622i
12.8	−0.502346	−	4.13719i	5.96938	+	2.26389i	−1.32894	+	0.327553i	−8.58865	−	4.50767i	6.36744	−	25.8337i	68.4200	+	25.9483i	−21.6228	−	57.0145i	−30.1211	−	26.6850i	−14.3346	+	37.7973i
12.9	−0.419088	−	3.45150i	−12.6530	−	4.79867i	3.79786	−	0.936088i	29.4454	+	15.4541i	−11.2599	+	45.6830i	78.2376	+	29.6716i	−24.5491	−	64.7306i	76.4429	+	67.7225i	40.9997	−	108.107i
12.10	−0.233315	−	1.92152i	−15.7837	−	5.98596i	11.8973	−	2.93241i	−12.0970	−	6.34898i	−7.81957	+	31.7252i	−70.4513	−	26.7186i	−19.3926	−	51.1342i	152.664	+	135.248i	−9.37728	+	24.7259i
12.11	−0.173468	−	1.42863i	6.53699	+	2.47915i	13.5242	−	3.33341i	−34.1964	−	17.9477i	2.40785	−	9.76902i	−59.0770	−	22.4049i	−15.2734	−	40.2725i	−24.0433	−	21.3005i	−19.7087	+	51.9675i
12.12	−0.131802	−	1.08548i	10.9130	+	4.13876i	14.3742	−	3.54291i	8.25526	+	4.33270i	3.05420	−	12.3914i	31.8441	+	12.0769i	−11.9442	−	31.4943i	41.3350	+	36.6196i	3.61501	−	9.53201i
12.13	0.0188772	+	0.155468i	−7.84131	−	2.97382i	15.5113	−	3.82318i	−24.6914	−	12.9591i	0.314310	−	1.27521i	42.2786	+	16.0341i	1.77574	+	4.68224i	−7.98675	−	7.07564i	1.54861	−	4.08335i
12.14	0.0344746	+	0.283924i	3.49904	+	1.32701i	15.4556	−	3.80947i	39.0664	+	20.5036i	−0.256143	+	1.03921i	−9.85170	−	3.73626i	3.23715	+	8.53568i	−50.1470	−	44.4264i	−4.47468	+	11.7988i
12.15	0.0505850	+	0.416605i	−8.05722	−	3.05570i	15.3641	−	3.78690i	10.7923	+	5.66421i	0.865446	−	3.51125i	−22.4759	−	8.52398i	4.73588	+	12.4875i	−5.04789	−	4.47204i	−1.81381	+	4.78263i
12.16	0.264349	+	2.17711i	−2.01838	−	0.765469i	10.8652	−	2.67802i	−12.7192	−	6.67557i	1.13295	−	4.59657i	44.8959	+	17.0268i	21.1455	+	55.7560i	−57.1415	−	50.6229i	11.1711	−	29.4558i
12.17	0.347113	+	2.85873i	14.7159	+	5.58100i	7.48322	−	1.84445i	−30.9987	−	16.2694i	−10.8465	+	44.0060i	42.9932	+	16.3052i	24.2089	+	63.8337i	124.780	+	110.546i	35.7497	−	94.2643i
12.18	0.486643	+	4.00786i	11.0169	+	4.17816i	−0.291090	+	0.0717472i	13.9031	+	7.29689i	−11.3842	+	46.1875i	−26.1724	−	9.92589i	22.4771	+	59.2673i	43.2855	+	38.3476i	−22.4791	+	59.2726i
12.19	0.495058	+	4.07717i	−12.1243	−	4.59813i	−0.843140	+	0.207815i	27.6718	+	14.5233i	12.7451	−	51.7090i	−7.53215	−	2.85657i	22.0377	+	58.1087i	65.2256	+	57.7849i	−45.5148	+	120.013i
12.20	0.498028	+	4.10163i	−0.324100	−	0.122915i	−1.04024	+	0.256397i	−12.1103	−	6.35598i	0.342740	−	1.39055i	−66.6642	−	25.2824i	21.8725	+	57.6731i	−60.5394	−	53.6333i	20.0386	−	52.8374i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
79.f	odd	26	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	79.5.f.a	✓	300
79.f	odd	26	1	inner	79.5.f.a	✓	300

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
79.5.f.a	✓	300	1.a	even	1	1	trivial
79.5.f.a	✓	300	79.f	odd	26	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(79, [\chi])\).