Newform orbit 64.5.j.a

• Label: 64.5.j.a
• Level: $64$
• Weight: $5$
• Character orbit: 64.j
• Analytic conductor: $6.616$
• Analytic rank: $0$
• Dimension: $248$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	64.j (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.61567763737\)
Analytic rank:	\(0\)
Dimension:	\(248\)
Relative dimension:	\(31\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 248 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−3.99297	−	0.236974i	−9.42585	−	1.87492i	15.8877	+	1.89246i	−18.1386	−	12.1198i	37.1929	+	9.72018i	−22.8124	−	55.0740i	−62.9907	−	11.3215i	10.4971	+	4.34804i	69.5549	+	52.6925i
3.2	−3.96804	−	0.504628i	9.60846	+	1.91124i	15.4907	+	4.00477i	22.8564	+	15.2722i	−37.1623	−	12.4326i	7.95054	+	19.1943i	−59.4468	−	23.7081i	13.8354	+	5.73079i	−82.9885	−	72.1346i
3.3	−3.78468	+	1.29468i	4.98643	+	0.991863i	12.6476	−	9.79988i	−24.9007	−	16.6381i	−20.1562	+	2.70193i	16.4913	+	39.8136i	−35.1796	+	53.4640i	−50.9535	−	21.1056i	115.782	+	30.7316i
3.4	−3.78335	+	1.29855i	−12.5808	−	2.50249i	12.6275	−	9.82575i	29.9674	+	20.0236i	50.8474	−	6.86907i	1.33932	+	3.23340i	−35.0152	+	53.5718i	77.1811	+	31.9694i	−139.379	−	36.8422i
3.5	−3.54845	−	1.84621i	−8.75290	−	1.74106i	9.18298	+	13.1024i	−0.0358229	−	0.0239361i	27.8449	+	22.3378i	25.8159	+	62.3250i	−8.39552	−	63.4469i	−1.25225	−	0.518697i	0.0829246	+	0.151073i
3.6	−3.42642	−	2.06389i	15.1223	+	3.00802i	7.48068	+	14.1435i	−36.5532	−	24.4241i	−45.6072	−	41.5176i	−17.3663	−	41.9260i	3.55879	−	63.9010i	144.802	+	59.9791i	74.8379	+	159.129i
3.7	−3.16807	+	2.44200i	3.85129	+	0.766070i	4.07327	−	15.4728i	6.53139	+	4.36414i	−14.0719	+	6.97790i	−24.1743	−	58.3618i	24.8802	+	58.9659i	−60.5886	−	25.0966i	−31.3491	+	2.12379i
3.8	−2.83859	−	2.81823i	0.198617	+	0.0395075i	0.115175	+	15.9996i	9.92813	+	6.63377i	−0.452452	−	0.671895i	−22.6838	−	54.7636i	44.7636	−	45.7408i	−74.7964	−	30.9817i	−9.48642	−	46.8103i
3.9	−2.31551	+	3.26166i	−11.3786	−	2.26335i	−5.27681	−	15.1048i	−21.6613	−	14.4736i	33.7297	−	31.8724i	10.7403	+	25.9293i	61.4852	+	17.7642i	49.5164	+	20.5104i	97.3652	−	37.1380i
3.10	−1.97915	+	3.47606i	15.6115	+	3.10532i	−8.16592	−	13.7593i	1.90371	+	1.27202i	−41.6917	+	48.1205i	16.4195	+	39.6401i	63.9896	−	1.15350i	159.241	+	65.9598i	−8.18934	+	4.09989i
3.11	−1.74404	−	3.59977i	3.11383	+	0.619379i	−9.91666	+	12.5563i	−22.4636	−	15.0097i	−3.20102	−	12.2893i	30.2368	+	72.9982i	62.4947	+	13.7991i	−65.5219	−	27.1401i	−14.8541	+	107.041i
3.12	−1.41579	+	3.74106i	−0.696393	−	0.138521i	−11.9911	−	10.5931i	34.3573	+	22.9568i	1.50416	−	2.40913i	9.09928	+	21.9676i	56.6064	−	29.8616i	−74.3685	−	30.8044i	−134.526	+	96.0306i
3.13	−1.35582	−	3.76321i	−16.3493	−	3.25209i	−12.3235	+	10.2045i	−31.6255	−	21.1315i	9.92853	+	65.9353i	−13.7727	−	33.2501i	55.1101	+	32.5404i	181.891	+	75.3416i	−36.6436	+	147.664i
3.14	−0.820674	−	3.91491i	14.7668	+	2.93729i	−14.6530	+	6.42572i	20.6310	+	13.7852i	−0.619474	−	60.2210i	4.32526	+	10.4421i	37.1814	+	52.0917i	134.595	+	55.7511i	37.0364	−	92.0816i
3.15	−0.766493	−	3.92587i	−9.15272	−	1.82059i	−14.8250	+	6.01831i	35.2609	+	23.5605i	−0.131913	+	37.3279i	0.0792910	+	0.191425i	34.9904	+	53.5880i	5.62349	+	2.32933i	65.4686	−	156.489i
3.16	−0.0333796	+	3.99986i	7.27231	+	1.44655i	−15.9978	−	0.267028i	−30.1748	−	20.1622i	−6.02876	+	29.0400i	−30.7281	−	74.1842i	1.60207	−	63.9799i	−24.0402	−	9.95778i	81.6530	−	120.022i
3.17	0.137597	+	3.99763i	−2.85073	−	0.567046i	−15.9621	+	1.10013i	−5.48438	−	3.66455i	1.87459	−	11.4742i	7.86809	+	18.9952i	−6.59425	−	63.6594i	−67.0291	−	27.7644i	13.8949	−	22.4288i
3.18	0.889585	+	3.89983i	−16.6130	−	3.30453i	−14.4173	+	6.93845i	15.9108	+	10.6312i	−1.89158	−	67.7274i	−20.4213	−	49.3014i	−39.8841	−	50.0525i	190.237	+	78.7990i	−27.3060	+	71.5066i
3.19	0.891042	−	3.89949i	4.41694	+	0.878584i	−14.4121	−	6.94923i	−11.2936	−	7.54612i	7.36171	−	16.4410i	−11.6857	−	28.2119i	−39.9402	+	50.0078i	−56.0968	−	23.2360i	−39.4891	+	37.3153i
3.20	1.80399	−	3.57010i	−9.86814	−	1.96290i	−9.49127	−	12.8808i	−2.30419	−	1.53961i	−24.8097	+	31.6892i	9.03309	+	21.8078i	−63.1080	+	10.6480i	18.6930	+	7.74290i	−9.65331	+	5.44877i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
64.j	odd	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	64.5.j.a	✓	248
64.j	odd	16	1	inner	64.5.j.a	✓	248

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
64.5.j.a	✓	248	1.a	even	1	1	trivial
64.5.j.a	✓	248	64.j	odd	16	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(64, [\chi])\).