Newform orbit 141.5.h.a

• Label: 141.5.h.a
• Level: $141$
• Weight: $5$
• Character orbit: 141.h
• Analytic conductor: $14.575$
• Analytic rank: $0$
• Dimension: $1364$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 141 = 3 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	141.h (of order \(46\), degree \(22\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.5751647948\)
Analytic rank:	\(0\)
Dimension:	\(1364\)
Relative dimension:	\(62\) over \(\Q(\zeta_{46})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{46}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1364 q - 31 q^{3} + 466 q^{4} - 55 q^{6} - 42 q^{7} - 191 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−1.04200	+	7.58108i	3.99631	+	8.06409i	−40.9803	−	11.4822i	1.08634	−	0.386084i	−65.2986	+	21.8936i	2.87149	−	41.9798i	80.9691	−	186.410i	−49.0590	+	64.4532i	1.79498	+	8.63791i
2.2	−1.03693	+	7.54425i	6.03841	−	6.67365i	−40.4339	−	11.3290i	−43.4071	+	15.4269i	44.0862	+	52.4755i	−1.55386	+	22.7166i	78.8540	−	181.540i	−8.07512	−	80.5965i	−71.3740	−	343.470i
2.3	−0.999896	+	7.27479i	−8.92319	+	1.17332i	−36.5160	−	10.2313i	−24.3625	+	8.65843i	0.386608	−	66.0875i	−2.56800	+	37.5428i	64.1343	−	147.652i	78.2466	−	20.9395i	−38.6282	−	185.889i
2.4	−0.971587	+	7.06882i	−7.91219	+	4.28921i	−33.6176	−	9.41921i	39.4887	−	14.0343i	−22.6323	−	60.0972i	0.965504	−	14.1152i	53.7619	−	123.772i	44.2053	−	67.8741i	60.8391	+	292.774i
2.5	−0.960238	+	6.98625i	−6.33826	−	6.38955i	−32.4789	−	9.10017i	1.04882	−	0.372752i	50.7253	−	38.1452i	3.59967	−	52.6252i	49.8116	−	114.678i	−0.652820	+	80.9974i	1.59702	+	7.68528i
2.6	−0.941621	+	6.85080i	8.99584	+	0.273712i	−30.6402	−	8.58498i	20.9501	−	7.44567i	−10.3458	+	61.3710i	−2.07116	+	30.2793i	43.5850	−	100.343i	80.8502	+	4.92453i	31.2818	+	150.536i
2.7	−0.939147	+	6.83280i	−0.241069	−	8.99677i	−30.3985	−	8.51727i	20.5834	−	7.31533i	61.6996	+	6.80211i	−3.80093	+	55.5676i	42.7809	−	98.4914i	−80.8838	+	4.33769i	30.6534	+	147.512i
2.8	−0.843927	+	6.14002i	−4.44169	+	7.82761i	−21.5810	−	6.04671i	−34.3836	+	12.2199i	−44.3132	−	33.8780i	4.01415	−	58.6849i	15.8327	−	36.4506i	−41.5429	−	69.5355i	−46.0135	−	221.429i
2.9	−0.841916	+	6.12540i	1.17508	+	8.92296i	−21.4050	−	5.99739i	−16.1790	+	5.75003i	−55.6460	−	0.314567i	−5.64399	+	82.5122i	15.3447	−	35.3269i	−78.2384	+	20.9703i	−21.5998	−	103.944i
2.10	−0.795405	+	5.78700i	8.20562	−	3.69701i	−17.4501	−	4.88928i	−4.83217	+	1.71736i	14.8678	+	50.4265i	5.00842	−	73.2205i	4.93855	−	11.3697i	53.6643	−	60.6724i	−6.09480	−	29.3298i
2.11	−0.750433	+	5.45980i	−0.681876	+	8.97413i	−13.8396	−	3.87769i	32.3643	−	11.5023i	−48.4853	−	10.4574i	−2.14095	+	31.2996i	−3.57315	+	8.22622i	−80.0701	−	12.2385i	38.5129	+	185.334i
2.12	−0.726412	+	5.28504i	1.40191	−	8.89014i	−11.9973	−	3.36148i	−7.76251	+	2.75880i	45.9664	+	13.8671i	2.12315	−	31.0394i	−7.52526	+	17.3249i	−77.0693	−	24.9264i	−8.94156	−	43.0292i
2.13	−0.716873	+	5.21564i	−8.55117	−	2.80670i	−11.2823	−	3.16114i	−0.715299	+	0.254217i	20.7688	−	42.5877i	−6.14264	+	89.8022i	−8.98388	+	20.6830i	65.2449	+	48.0011i	−0.813127	−	3.91298i
2.14	−0.651455	+	4.73969i	7.90075	+	4.31023i	−6.63357	−	1.85864i	−24.7155	+	8.78388i	−25.5761	+	34.6392i	−0.928731	+	13.5776i	−17.3660	+	39.9804i	43.8438	+	68.1081i	−25.5318	−	122.866i
2.15	−0.639926	+	4.65580i	−6.81649	+	5.87668i	−5.86033	−	1.64199i	−2.40994	+	0.856494i	−22.9986	−	35.4969i	1.19123	−	17.4152i	−18.5621	+	42.7343i	11.9292	−	80.1168i	−2.44548	−	11.7683i
2.16	−0.599436	+	4.36122i	5.85171	−	6.83794i	−3.25422	−	0.911789i	40.7331	−	14.4766i	26.3140	+	29.6195i	0.451984	−	6.60777i	−22.1344	+	50.9585i	−12.5149	−	80.0274i	38.7185	+	186.324i
2.17	−0.584158	+	4.25007i	−5.97246	−	6.73273i	−2.31514	−	0.648672i	−43.7173	+	15.5371i	32.1034	−	21.4504i	−0.106030	+	1.55011i	−23.2371	+	53.4972i	−9.65935	+	80.4220i	−40.4961	−	194.878i
2.18	−0.560414	+	4.07731i	5.37575	+	7.21812i	−0.903754	−	0.253220i	25.4855	−	9.05755i	−32.4432	+	17.8735i	6.64507	−	97.1474i	−24.6959	+	56.8557i	−23.2026	+	77.6057i	22.6481	+	108.988i
2.19	−0.531866	+	3.86961i	−7.29133	−	5.27603i	0.715659	+	0.200518i	37.2051	−	13.2227i	24.2942	−	25.4085i	4.24193	−	62.0148i	−26.0550	+	59.9846i	25.3271	+	76.9385i	31.3786	+	151.002i
2.20	−0.470536	+	3.42340i	−8.98979	+	0.428640i	3.90839	+	1.09508i	8.30722	−	2.95239i	2.76261	−	30.9774i	0.0200721	−	0.293444i	−27.6153	+	63.5768i	80.6325	−	7.70676i	6.19836	+	29.8282i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
47.c	even	23	1	inner
141.h	odd	46	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	141.5.h.a	✓	1364
3.b	odd	2	1	inner	141.5.h.a	✓	1364
47.c	even	23	1	inner	141.5.h.a	✓	1364
141.h	odd	46	1	inner	141.5.h.a	✓	1364

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
141.5.h.a	✓	1364	1.a	even	1	1	trivial
141.5.h.a	✓	1364	3.b	odd	2	1	inner
141.5.h.a	✓	1364	47.c	even	23	1	inner
141.5.h.a	✓	1364	141.h	odd	46	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(141, [\chi])\).