Newform orbit 102.5.j.a

• Label: 102.5.j.a
• Level: $102$
• Weight: $5$
• Character orbit: 102.j
• Analytic conductor: $10.544$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	102.j (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.5437362346\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(6\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 192 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−1.08239	+	2.61313i	−2.88683	+	4.32044i	−5.65685	−	5.65685i	−6.12451	−	30.7900i	−8.16518	−	12.2201i	−10.5056	+	52.8150i	20.9050	−	8.65914i	−10.3325	−	24.9447i	87.0872	+	17.3227i
7.2	−1.08239	+	2.61313i	−2.88683	+	4.32044i	−5.65685	−	5.65685i	2.20133	+	11.0668i	−8.16518	−	12.2201i	15.9065	−	79.9675i	20.9050	−	8.65914i	−10.3325	−	24.9447i	−31.3017	−	6.22629i
7.3	−1.08239	+	2.61313i	−2.88683	+	4.32044i	−5.65685	−	5.65685i	4.20586	+	21.1443i	−8.16518	−	12.2201i	−11.2322	+	56.4682i	20.9050	−	8.65914i	−10.3325	−	24.9447i	−59.8051	−	11.8960i
7.4	−1.08239	+	2.61313i	2.88683	−	4.32044i	−5.65685	−	5.65685i	−8.09386	−	40.6906i	8.16518	+	12.2201i	−5.91768	+	29.7502i	20.9050	−	8.65914i	−10.3325	−	24.9447i	115.090	+	22.8929i
7.5	−1.08239	+	2.61313i	2.88683	−	4.32044i	−5.65685	−	5.65685i	−0.548867	−	2.75934i	8.16518	+	12.2201i	−5.21139	+	26.1994i	20.9050	−	8.65914i	−10.3325	−	24.9447i	7.80460	+	1.55243i
7.6	−1.08239	+	2.61313i	2.88683	−	4.32044i	−5.65685	−	5.65685i	6.59215	+	33.1410i	8.16518	+	12.2201i	−0.554149	+	2.78589i	20.9050	−	8.65914i	−10.3325	−	24.9447i	−93.7369	−	18.6454i
31.1	2.61313	−	1.08239i	−1.01372	+	5.09631i	5.65685	−	5.65685i	−22.4428	+	14.9958i	2.86723	+	14.4145i	−25.8791	−	17.2919i	8.65914	−	20.9050i	−24.9447	−	10.3325i	−42.4145	+	63.4777i
31.2	2.61313	−	1.08239i	−1.01372	+	5.09631i	5.65685	−	5.65685i	13.2500	−	8.85336i	2.86723	+	14.4145i	42.7276	+	28.5496i	8.65914	−	20.9050i	−24.9447	−	10.3325i	25.0411	−	37.4766i
31.3	2.61313	−	1.08239i	−1.01372	+	5.09631i	5.65685	−	5.65685i	28.3496	−	18.9426i	2.86723	+	14.4145i	−79.4999	−	53.1201i	8.65914	−	20.9050i	−24.9447	−	10.3325i	53.5778	−	80.1848i
31.4	2.61313	−	1.08239i	1.01372	−	5.09631i	5.65685	−	5.65685i	−13.6432	+	9.11609i	−2.86723	−	14.4145i	−57.0872	−	38.1444i	8.65914	−	20.9050i	−24.9447	−	10.3325i	−25.7842	+	38.5888i
31.5	2.61313	−	1.08239i	1.01372	−	5.09631i	5.65685	−	5.65685i	5.54712	−	3.70646i	−2.86723	−	14.4145i	64.8753	+	43.3483i	8.65914	−	20.9050i	−24.9447	−	10.3325i	10.4835	−	15.6896i
31.6	2.61313	−	1.08239i	1.01372	−	5.09631i	5.65685	−	5.65685i	34.9446	−	23.3492i	−2.86723	−	14.4145i	−10.2269	−	6.83341i	8.65914	−	20.9050i	−24.9447	−	10.3325i	66.0415	−	98.8381i
37.1	−2.61313	+	1.08239i	−5.09631	−	1.01372i	5.65685	−	5.65685i	−26.9948	−	40.4005i	14.4145	−	2.86723i	26.4277	−	39.5518i	−8.65914	+	20.9050i	24.9447	+	10.3325i	114.270	+	76.3527i
37.2	−2.61313	+	1.08239i	−5.09631	−	1.01372i	5.65685	−	5.65685i	−0.395218	−	0.591485i	14.4145	−	2.86723i	−25.0622	+	37.5082i	−8.65914	+	20.9050i	24.9447	+	10.3325i	1.67297	+	1.11784i
37.3	−2.61313	+	1.08239i	−5.09631	−	1.01372i	5.65685	−	5.65685i	0.556206	+	0.832421i	14.4145	−	2.86723i	6.08279	−	9.10353i	−8.65914	+	20.9050i	24.9447	+	10.3325i	−2.35444	−	1.57319i
37.4	−2.61313	+	1.08239i	5.09631	+	1.01372i	5.65685	−	5.65685i	−26.1187	−	39.0895i	−14.4145	+	2.86723i	−35.4494	+	53.0538i	−8.65914	+	20.9050i	24.9447	+	10.3325i	110.562	+	73.8750i
37.5	−2.61313	+	1.08239i	5.09631	+	1.01372i	5.65685	−	5.65685i	−2.11072	−	3.15892i	−14.4145	+	2.86723i	16.5199	−	24.7238i	−8.65914	+	20.9050i	24.9447	+	10.3325i	8.93478	+	5.97003i
37.6	−2.61313	+	1.08239i	5.09631	+	1.01372i	5.65685	−	5.65685i	23.2000	+	34.7213i	−14.4145	+	2.86723i	−13.8550	+	20.7355i	−8.65914	+	20.9050i	24.9447	+	10.3325i	−98.2067	−	65.6196i
61.1	1.08239	−	2.61313i	−4.32044	−	2.88683i	−5.65685	−	5.65685i	−23.5274	+	4.67988i	−12.2201	+	8.16518i	2.86555	+	0.569993i	−20.9050	+	8.65914i	10.3325	+	24.9447i	−13.2367	+	66.5455i
61.2	1.08239	−	2.61313i	−4.32044	−	2.88683i	−5.65685	−	5.65685i	10.7984	−	2.14793i	−12.2201	+	8.16518i	−41.2988	−	8.21484i	−20.9050	+	8.65914i	10.3325	+	24.9447i	6.07525	−	30.5424i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.e	odd	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	102.5.j.a	✓	48
17.e	odd	16	1	inner	102.5.j.a	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
102.5.j.a	✓	48	1.a	even	1	1	trivial
102.5.j.a	✓	48	17.e	odd	16	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^48 + 2200*T5^46 - 110064*T5^45 + 6056896*T5^44 - 123508400*T5^43 + 9690647544*T5^42 - 199214436240*T5^41 + 3146286060608*T5^40 + 156340076589072*T5^39 - 1808050801143128*T5^38 + 322814925805331440*T5^37 - 20453791085754440024*T5^36 - 130251131959967005152*T5^35 + 10738426424264897432440*T5^34 - 189827249811183866291168*T5^33 + 27134134461653288537402409*T5^32 + 531525797898813076850568704*T5^31 - 12409950589674214203021184944*T5^30 + 51211554634869543656850040144*T5^29 + 6732994193663803379255690359736*T5^28 + 508800955235120308384033430561568*T5^27 + 42328321769775831152469818288391072*T5^26 + 690634886025715788635662100774985504*T5^25 - 14316667394196458949289722637801184*T5^24 + 177401062513069119012240894855379550016*T5^23 + 561105643857972812549502393634662416352*T5^22 - 97776405516868049604768016615291423047008*T5^21 + 1136120061778798165361358959201942597048432*T5^20 + 33481034801953566169614274482378547069998144*T5^19 - 185819647792344805773038293670354185351129792*T5^18 - 4084252150636726465523139281533514100361565696*T5^17 + 46655963149937966845601358921150099264461966232*T5^16 - 567213019889121456497665219122015045071198564352*T5^15 - 2537415887308506353370852842103050953076404864576*T5^14 + 80322338242378805241754575613815497966590777777728*T5^13 + 99224988337606148186779271244717843284350493425248*T5^12 - 2122669185359091554359562496840019781073827521204352*T5^11 + 23683624059716900000583481893568745689147682291456*T5^10 + 32358509946574673543101913688437598749968410938456448*T5^9 + 397686610755495096479687501701778690962087195819819136*T5^8 + 892506318649663069092546866212493743010940079476325376*T5^7 + 2854776120124678871882239653486085471358870319722918144*T5^6 + 1510043235356753060001823379627563815879724450220658560*T5^5 + 2008775903680904659050926611337776634212121545956024384*T5^4 + 2157914142534696047243590507109351114405308898806726400*T5^3 + 2049449305929795267383256901378137031119273528929125760*T5^2 + 930846571080855761852544562222257337693755604803311104*T5 + 145662631519367400878515263453816052572731139767339536