Newform orbit 92.5.g.a

• Label: 92.5.g.a
• Level: $92$
• Weight: $5$
• Character orbit: 92.g
• Analytic conductor: $9.510$
• Analytic rank: $0$
• Dimension: $460$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(9.51003660371\)
Analytic rank:	\(0\)
Dimension:	\(460\)
Relative dimension:	\(46\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9}+O(q^{10}) \)

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	−3.96913	−	0.495996i	−1.58323	−	0.723036i	15.5080	+	3.93734i	4.45073	−	5.13641i	5.92542	+	3.65510i	29.4250	+	45.7862i	−59.6003	−	23.3197i	−51.0599	−	58.9263i	−20.2131	+	18.1795i
3.2	−3.92455	+	0.773226i	9.14569	+	4.17669i	14.8042	−	6.06914i	−16.1904	+	18.6847i	−39.1223	−	9.31998i	−40.2835	−	62.6823i	−53.4072	+	35.2657i	13.1551	+	15.1818i	49.0925	−	85.8479i
3.3	−3.88066	−	0.969802i	−9.89031	−	4.51675i	14.1190	+	7.52693i	0.403340	−	0.465480i	34.0005	+	27.1196i	−44.1465	−	68.6932i	−47.4912	−	42.9020i	24.3734	+	28.1285i	−2.01665	+	1.41521i
3.4	−3.81343	+	1.20738i	−14.9199	−	6.81367i	13.0845	−	9.20851i	−23.3579	+	26.9564i	65.1225	+	7.96951i	36.5671	+	56.8995i	−38.7785	+	50.9139i	123.132	+	142.102i	56.5269	−	130.998i
3.5	−3.80469	−	1.23465i	9.38097	+	4.28415i	12.9513	+	9.39491i	27.9778	−	32.2881i	−30.4022	−	27.8821i	−26.7810	−	41.6720i	−37.6761	−	51.7350i	16.6050	+	19.1632i	−146.311	+	88.3034i
3.6	−3.79675	+	1.25886i	−8.69828	−	3.97237i	12.8306	−	9.55912i	17.8389	−	20.5871i	38.0258	+	4.13220i	−0.355839	−	0.553696i	−36.6808	+	52.4454i	6.83659	+	7.88985i	−41.8134	+	100.621i
3.7	−3.76171	+	1.35996i	10.4783	+	4.78529i	12.3010	−	10.2316i	−2.29468	+	2.64821i	−45.9243	−	3.75076i	24.1964	+	37.6503i	−32.3583	+	55.2172i	33.8526	+	39.0680i	5.03048	−	13.0825i
3.8	−3.75361	−	1.38217i	0.764490	+	0.349131i	12.1792	+	10.3763i	−30.5134	+	35.2144i	−2.38704	−	2.36716i	11.6504	+	18.1284i	−31.3743	−	55.7822i	−52.5812	−	60.6819i	163.208	−	90.0063i
3.9	−3.28360	+	2.28429i	2.55088	+	1.16495i	5.56402	−	15.0014i	24.3881	−	28.1454i	−11.0372	+	2.00174i	6.42136	+	9.99183i	15.9975	+	61.9684i	−47.8938	−	55.2724i	−15.7885	+	148.128i
3.10	−3.27248	−	2.30019i	15.9198	+	7.27032i	5.41821	+	15.0547i	−9.68558	+	11.1778i	−35.3740	−	60.4105i	30.2516	+	47.0723i	16.8977	−	61.7290i	147.538	+	170.268i	57.4069	−	14.3002i
3.11	−2.96738	+	2.68229i	−4.62172	−	2.11067i	1.61066	−	15.9187i	−13.3793	+	15.4406i	19.3758	−	6.13364i	−22.6762	−	35.2848i	37.9192	+	51.5571i	−36.1383	−	41.7058i	−1.71453	−	81.7053i
3.12	−2.93523	−	2.71744i	−14.4864	−	6.61573i	1.23109	+	15.9526i	17.8216	−	20.5672i	24.5431	+	58.7846i	31.8403	+	49.5444i	39.7365	−	50.1698i	113.045	+	130.461i	−108.200	+	11.9404i
3.13	−2.78224	−	2.87387i	−0.757494	−	0.345936i	−0.518302	+	15.9916i	5.96608	−	6.88523i	1.11335	+	3.13942i	8.51773	+	13.2539i	47.3999	−	43.0029i	−52.5896	−	60.6916i	−36.3863	+	2.01057i
3.14	−2.32421	−	3.25547i	8.11165	+	3.70447i	−5.19613	+	15.1328i	−5.11275	+	5.90043i	−6.79338	−	35.0171i	−24.7572	−	38.5230i	61.3410	−	18.2558i	−0.967950	−	1.11707i	31.0917	+	2.93057i
3.15	−2.10264	+	3.40278i	14.7279	+	6.72602i	−7.15784	−	14.3096i	12.7028	−	14.6598i	−53.8546	+	35.9735i	−0.00349382	−	0.00543649i	63.7429	+	5.73140i	118.629	+	136.905i	23.1747	+	74.0490i
3.16	−2.05277	−	3.43309i	−10.8750	−	4.96644i	−7.57227	+	14.0947i	−26.3181	+	30.3727i	5.27360	+	47.5298i	−20.2187	−	31.4609i	63.9326	−	2.93690i	40.5561	+	46.8042i	158.297	+	28.0043i
3.17	−2.05018	+	3.43464i	2.52708	+	1.15408i	−7.59355	−	14.0833i	−19.5042	+	22.5090i	−9.14482	+	6.31356i	36.1006	+	56.1736i	63.9391	+	2.79203i	−47.9895	−	55.3828i	−37.3235	−	113.138i
3.18	−1.63751	+	3.64946i	−12.3102	−	5.62186i	−10.6371	−	11.9521i	14.4068	−	16.6263i	40.6748	−	35.7195i	−4.73037	−	7.36060i	61.0370	−	19.2481i	66.8908	+	77.1961i	37.0857	+	79.8026i
3.19	−1.03186	+	3.86462i	6.26873	+	2.86283i	−13.8705	−	7.97547i	0.489836	−	0.565301i	−17.5322	+	21.2722i	−40.7053	−	63.3387i	45.1346	−	45.3748i	−21.9425	−	25.3230i	1.67923	+	2.47634i
3.20	−0.703907	−	3.93758i	8.34098	+	3.80920i	−15.0090	+	5.54338i	28.4399	−	32.8214i	9.12773	−	35.5246i	45.7110	+	71.1278i	32.3924	+	55.1972i	2.01818	+	2.32910i	−149.256	−	88.8812i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
23.c	even	11	1	inner
92.g	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.g.a	✓	460
4.b	odd	2	1	inner	92.5.g.a	✓	460
23.c	even	11	1	inner	92.5.g.a	✓	460
92.g	odd	22	1	inner	92.5.g.a	✓	460

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.5.g.a	✓	460	1.a	even	1	1	trivial
92.5.g.a	✓	460	4.b	odd	2	1	inner
92.5.g.a	✓	460	23.c	even	11	1	inner
92.5.g.a	✓	460	92.g	odd	22	1	inner

Hecke kernels

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