Newform orbit 102.5.j.b

• Label: 102.5.j.b
• 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	−7.28718	−	36.6351i	8.16518	+	12.2201i	−14.4024	+	72.4056i	−20.9050	+	8.65914i	−10.3325	−	24.9447i	−103.620	−	20.6112i
7.2	1.08239	−	2.61313i	−2.88683	+	4.32044i	−5.65685	−	5.65685i	1.92447	+	9.67498i	8.16518	+	12.2201i	4.19253	−	21.0773i	−20.9050	+	8.65914i	−10.3325	−	24.9447i	27.3650	+	5.44323i
7.3	1.08239	−	2.61313i	−2.88683	+	4.32044i	−5.65685	−	5.65685i	4.64519	+	23.3530i	8.16518	+	12.2201i	9.53792	−	47.9504i	−20.9050	+	8.65914i	−10.3325	−	24.9447i	66.0522	+	13.1386i
7.4	1.08239	−	2.61313i	2.88683	−	4.32044i	−5.65685	−	5.65685i	−4.19822	−	21.1059i	−8.16518	−	12.2201i	3.46582	−	17.4238i	−20.9050	+	8.65914i	−10.3325	−	24.9447i	−59.6964	−	11.8744i
7.5	1.08239	−	2.61313i	2.88683	−	4.32044i	−5.65685	−	5.65685i	6.36103	+	31.9791i	−8.16518	−	12.2201i	−14.0520	+	70.6441i	−20.9050	+	8.65914i	−10.3325	−	24.9447i	90.4505	+	17.9917i
7.6	1.08239	−	2.61313i	2.88683	−	4.32044i	−5.65685	−	5.65685i	8.91430	+	44.8152i	−8.16518	−	12.2201i	15.7662	−	79.2620i	−20.9050	+	8.65914i	−10.3325	−	24.9447i	126.757	+	25.2134i
31.1	−2.61313	+	1.08239i	−1.01372	+	5.09631i	5.65685	−	5.65685i	−31.9288	+	21.3342i	−2.86723	−	14.4145i	62.3427	+	41.6561i	−8.65914	+	20.9050i	−24.9447	−	10.3325i	60.3421	−	90.3083i
31.2	−2.61313	+	1.08239i	−1.01372	+	5.09631i	5.65685	−	5.65685i	4.05364	−	2.70856i	−2.86723	−	14.4145i	17.1513	+	11.4601i	−8.65914	+	20.9050i	−24.9447	−	10.3325i	−7.66095	+	11.4654i
31.3	−2.61313	+	1.08239i	−1.01372	+	5.09631i	5.65685	−	5.65685i	26.7045	−	17.8434i	−2.86723	−	14.4145i	−26.5753	−	17.7571i	−8.65914	+	20.9050i	−24.9447	−	10.3325i	−50.4686	+	75.5316i
31.4	−2.61313	+	1.08239i	1.01372	−	5.09631i	5.65685	−	5.65685i	−13.2554	+	8.85698i	2.86723	+	14.4145i	12.0897	+	8.07806i	−8.65914	+	20.9050i	−24.9447	−	10.3325i	25.0513	−	37.4919i
31.5	−2.61313	+	1.08239i	1.01372	−	5.09631i	5.65685	−	5.65685i	7.10823	−	4.74957i	2.86723	+	14.4145i	−54.8957	−	36.6801i	−8.65914	+	20.9050i	−24.9447	−	10.3325i	−13.4338	+	20.1051i
31.6	−2.61313	+	1.08239i	1.01372	−	5.09631i	5.65685	−	5.65685i	37.6090	−	25.1295i	2.86723	+	14.4145i	35.5121	+	23.7285i	−8.65914	+	20.9050i	−24.9447	−	10.3325i	−71.0770	+	106.374i
37.1	2.61313	−	1.08239i	−5.09631	−	1.01372i	5.65685	−	5.65685i	−14.6515	−	21.9275i	−14.4145	+	2.86723i	−46.2737	+	69.2535i	8.65914	−	20.9050i	24.9447	+	10.3325i	−62.0204	−	41.4407i
37.2	2.61313	−	1.08239i	−5.09631	−	1.01372i	5.65685	−	5.65685i	0.167997	+	0.251425i	−14.4145	+	2.86723i	13.2429	−	19.8193i	8.65914	−	20.9050i	24.9447	+	10.3325i	0.711138	+	0.475167i
37.3	2.61313	−	1.08239i	−5.09631	−	1.01372i	5.65685	−	5.65685i	15.1531	+	22.6781i	−14.4145	+	2.86723i	−7.11117	+	10.6426i	8.65914	−	20.9050i	24.9447	+	10.3325i	64.1435	+	42.8593i
37.4	2.61313	−	1.08239i	5.09631	+	1.01372i	5.65685	−	5.65685i	−19.6150	−	29.3559i	14.4145	−	2.86723i	10.9800	−	16.4328i	8.65914	−	20.9050i	24.9447	+	10.3325i	−83.0310	−	55.4795i
37.5	2.61313	−	1.08239i	5.09631	+	1.01372i	5.65685	−	5.65685i	6.01473	+	9.00168i	14.4145	−	2.86723i	26.3581	−	39.4477i	8.65914	−	20.9050i	24.9447	+	10.3325i	25.4606	+	17.0122i
37.6	2.61313	−	1.08239i	5.09631	+	1.01372i	5.65685	−	5.65685i	19.4092	+	29.0479i	14.4145	−	2.86723i	−37.2473	+	55.7446i	8.65914	−	20.9050i	24.9447	+	10.3325i	82.1598	+	54.8974i
61.1	−1.08239	+	2.61313i	−4.32044	−	2.88683i	−5.65685	−	5.65685i	−37.0952	+	7.37870i	12.2201	−	8.16518i	−15.3254	−	3.04841i	20.9050	−	8.65914i	10.3325	+	24.9447i	20.8701	−	104.921i
61.2	−1.08239	+	2.61313i	−4.32044	−	2.88683i	−5.65685	−	5.65685i	−13.2070	+	2.62704i	12.2201	−	8.16518i	90.5980	+	18.0211i	20.9050	−	8.65914i	10.3325	+	24.9447i	7.43038	−	37.3550i

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.b	✓	48
17.e	odd	16	1	inner	102.5.j.b	✓	48

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^48 + 1816*T5^46 + 80016*T5^45 + 1758016*T5^44 + 166878800*T5^43 + 8172073848*T5^42 + 335214327024*T5^41 + 15033000807488*T5^40 + 546510279792912*T5^39 + 18319824044592040*T5^38 + 715115984075403248*T5^37 + 21054275161859101864*T5^36 + 548973176784088401696*T5^35 + 18875473291181161657720*T5^34 + 339957225834780644775200*T5^33 + 21625691008887771890642217*T5^32 - 32432675260392072276412928*T5^31 + 12061126646783490554802368976*T5^30 + 271114356515383269539094576848*T5^29 - 12964967003691805611132583007176*T5^28 + 177503820832650208743012838684704*T5^27 - 5882135432058125502055670716613088*T5^26 - 50179233792365101341165359472937824*T5^25 + 112110775583464501211083249877970208*T5^24 - 141245028517765274392370256047743449792*T5^23 + 6108262605403426253430529512916347666912*T5^22 - 121972306634300301236913589418710423379296*T5^21 + 3323216895157151664283019831555226337304432*T5^20 - 17900463452233270430756360899388351602666944*T5^19 - 89281601815344379418093434928152179989522368*T5^18 + 1994708422442607926830441759424102049363723008*T5^17 - 211163048085237685996817046723907870432004191848*T5^16 - 1536151208532011384427453039666812510760210186240*T5^15 + 97787925099676028142601083030287549343435851630528*T5^14 - 470633443574042342007600995780032505205653976232896*T5^13 - 12946639149613766373068436259385187476059903337785248*T5^12 + 297210546113608150658148819936488468491241459383604096*T5^11 - 1029637531769229873573217750210018607553498064609869568*T5^10 - 22486015177735616081004632114245236400973032282027559040*T5^9 + 431574861702060122067946027862422616592557840954402746496*T5^8 - 2850296919244428183515460181695713760928394380946412870656*T5^7 + 2665980782257070559533725306641810035379769931102219856128*T5^6 + 102827428035107425852997499556037817064204215561898095169408*T5^5 - 402224281160960695317813866690706575918311978972731980415936*T5^4 - 593679871057156829934053080439982499149107058035395223001344*T5^3 + 6491597503818292921328848814359986917581339241934944324145536*T5^2 - 2176839625813889324075572908448038487353586440817508315903488*T5 + 574324666195644461008670086900361000068432549285363748467216