Newform orbit 92.5.f.a

• Label: 92.5.f.a
• Level: $92$
• Weight: $5$
• Character orbit: 92.f
• Analytic conductor: $9.510$
• Analytic rank: $0$
• Dimension: $80$
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$92 = 2^{2} \cdot 23$
Weight:	$k$	$=$	$5$
Character orbit:	$[\chi]$	$=$	92.f (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 80 * q + 10 * q^3 - 318 * q^9 + 2 * q^13 + 1463 * q^15 - 495 * q^17 - 957 * q^19 - 1353 * q^21 + 1614 * q^23 + 1890 * q^25 + 4723 * q^27 - 1617 * q^29 - 3271 * q^31 - 6655 * q^33 - 5280 * q^35 + 3520 * q^37 + 6138 * q^39 + 11370 * q^41 + 7216 * q^43 - 270 * q^47 - 14512 * q^49 - 17424 * q^51 - 7392 * q^53 + 5746 * q^55 + 18381 * q^57 + 11772 * q^59 - 22484 * q^61 - 27775 * q^63 - 27951 * q^65 - 2926 * q^67 + 15769 * q^69 + 19779 * q^71 + 24400 * q^73 + 2809 * q^75 + 19839 * q^77 + 21604 * q^79 + 22224 * q^81 - 11253 * q^83 - 25594 * q^85 + 45506 * q^87 + 7656 * q^89 + 7970 * q^93 - 22437 * q^95 + 32439 * q^97 - 48477 * q^99

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
5.1		0		−10.2373	+	11.8144i		0		−30.5407	−	4.39110i		0		−13.3522	+	6.09777i		0		−23.2517	−	161.719i		0
5.2		0		−6.76620	+	7.80861i		0		32.0322	+	4.60554i		0		17.3862	−	7.93999i		0		−3.66545	−	25.4937i		0
5.3		0		−4.95559	+	5.71906i		0		−3.34342	−	0.480711i		0		−14.6603	+	6.69511i		0		3.37777	+	23.4929i		0
5.4		0		0.325960	−	0.376178i		0		−35.7139	−	5.13488i		0		57.8313	−	26.4107i		0		11.4922	+	79.9303i		0
5.5		0		3.01425	−	3.47863i		0		7.38497	+	1.06180i		0		35.2368	−	16.0921i		0		8.51233	+	59.2046i		0
5.6		0		3.34179	−	3.85663i		0		−4.69485	−	0.675018i		0		−82.0191	+	37.4569i		0		7.82145	+	54.3994i		0
5.7		0		7.42513	−	8.56905i		0		47.6796	+	6.85529i		0		11.7029	−	5.34454i		0		−6.76867	−	47.0771i		0
5.8		0		10.5723	−	12.2011i		0		−24.5957	−	3.53633i		0		14.8856	−	6.79802i		0		−25.5654	−	177.811i		0
17.1		0		−13.2407	−	3.88781i		0		4.37705	+	6.81083i		0		−71.4769	−	10.2768i		0		92.0587	+	59.1625i		0
17.2		0		−9.91432	−	2.91111i		0		−22.1926	−	34.5324i		0		38.0772	+	5.47467i		0		21.6776	+	13.9314i		0
17.3		0		−9.85031	−	2.89231i		0		8.29543	+	12.9079i		0		46.9607	+	6.75193i		0		20.5215	+	13.1884i		0
17.4		0		0.536308	+	0.157474i		0		3.14686	+	4.89660i		0		−55.6751	−	8.00488i		0		−67.8787	−	43.6230i		0
17.5		0		2.34060	+	0.687262i		0		21.9968	+	34.2277i		0		22.5786	+	3.24631i		0		−63.1355	−	40.5747i		0
17.6		0		4.86802	+	1.42938i		0		−8.73770	−	13.5961i		0		51.3576	+	7.38410i		0		−46.4871	−	29.8754i		0
17.7		0		8.15848	+	2.39555i		0		−18.7036	−	29.1033i		0		−54.6689	−	7.86020i		0		−7.31931	−	4.70383i		0
17.8		0		15.7364	+	4.62062i		0		6.12535	+	9.53123i		0		6.79278	+	0.976655i		0		158.142	+	101.632i		0
21.1		0		−2.44568	−	17.0101i		0		−12.8263	+	43.6825i		0		44.6142	+	38.6584i		0		−205.644	+	60.3824i		0
21.2		0		−1.70114	−	11.8317i		0		6.41533	−	21.8486i		0		−35.1057	−	30.4192i		0		−59.3762	+	17.4344i		0
21.3		0		−0.996463	−	6.93055i		0		5.74873	−	19.5784i		0		56.9158	+	49.3178i		0		30.6793	−	9.00825i		0
21.4		0		−0.369021	−	2.56660i		0		−3.51259	+	11.9628i		0		−6.50335	−	5.63519i		0		71.2677	−	20.9261i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.d	odd	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	92.5.f.a	✓	80
23.d	odd	22	1	inner	92.5.f.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.5.f.a	✓	80	1.a	even	1	1	trivial
92.5.f.a	✓	80	23.d	odd	22	1	inner

Hecke kernels

This newform subspace is the entire newspace $S_{5}^{\mathrm{new}}(92, [\chi])$.