Newform orbit 143.4.u.a

• Label: 143.4.u.a
• Level: $143$
• Weight: $4$
• Character orbit: 143.u
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $320$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.u (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(320\)
Relative dimension:	\(40\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 320 q - 9 q^{2} - 3 q^{3} - 155 q^{4} - 9 q^{6} - 9 q^{7} + 273 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−2.23181	−	5.01274i	5.63398	+	6.25717i	−14.7935	+	16.4298i	−7.72452	−	10.6319i	18.7916	−	42.2065i	0.606706	+	0.546280i	73.6262	+	23.9226i	−4.58817	+	43.6535i	−36.0551	+	62.4493i
4.2	−2.20175	−	4.94522i	−2.15581	−	2.39427i	−14.2544	+	15.8312i	−0.971003	−	1.33647i	−7.09362	+	15.9325i	20.8231	+	18.7492i	68.4872	+	22.2528i	1.73726	−	16.5289i	−4.47123	+	7.74441i
4.3	−1.99780	−	4.48714i	−6.45875	−	7.17317i	−10.7902	+	11.9837i	−2.84019	−	3.90918i	−19.2837	+	43.3119i	−18.9906	−	17.0992i	37.9580	+	12.3333i	−6.91663	+	65.8073i	−11.8669	+	20.5541i
4.4	−1.94565	−	4.36999i	−0.542250	−	0.602229i	−9.95824	+	11.0597i	−2.55676	−	3.51908i	−1.57671	+	3.54135i	−24.3125	−	21.8910i	31.3108	+	10.1735i	2.75362	−	26.1990i	−10.4038	+	18.0199i
4.5	−1.90042	−	4.26841i	−2.73419	−	3.03663i	−9.25466	+	10.2783i	11.5237	+	15.8610i	−7.76545	+	17.4415i	3.10122	+	2.79235i	25.9105	+	8.41882i	1.07697	−	10.2467i	45.8015	−	79.3305i
4.6	−1.89534	−	4.25700i	2.25759	+	2.50731i	−9.17670	+	10.1918i	2.62986	+	3.61970i	6.39472	−	14.3628i	−0.236753	−	0.213173i	25.3249	+	8.22857i	1.63239	−	15.5311i	10.4246	−	18.0559i
4.7	−1.64185	−	3.68765i	5.36113	+	5.95413i	−5.55003	+	6.16393i	9.43899	+	12.9917i	13.1546	−	29.5457i	−10.4423	−	9.40233i	1.13017	+	0.367215i	−3.88777	+	36.9897i	32.4113	−	56.1380i
4.8	−1.53323	−	3.44370i	0.552069	+	0.613135i	−4.15522	+	4.61484i	−11.7724	−	16.2033i	1.26500	−	2.84124i	4.19660	+	3.77864i	−6.41775	−	2.08525i	2.75111	−	26.1751i	−37.7495	+	65.3840i
4.9	−1.41447	−	3.17694i	5.00365	+	5.55711i	−2.73920	+	3.04219i	0.947657	+	1.30434i	10.5771	−	23.7566i	21.7207	+	19.5574i	−12.9197	−	4.19788i	−3.02275	+	28.7595i	2.80338	−	4.85559i
4.10	−1.37767	−	3.09430i	−3.60199	−	4.00042i	−2.32366	+	2.58069i	−9.60115	−	13.2148i	−7.41612	+	16.6569i	5.47931	+	4.93359i	−14.5842	−	4.73868i	−0.206722	+	1.96683i	−27.6635	+	47.9145i
4.11	−1.32689	−	2.98024i	−5.91577	−	6.57013i	−1.76817	+	1.96375i	2.51857	+	3.46651i	−11.7310	+	26.3483i	14.6945	+	13.2310i	−16.6223	−	5.40091i	−5.34798	+	50.8826i	6.98918	−	12.1056i
4.12	−1.20352	−	2.70315i	0.816949	+	0.907313i	−0.505496	+	0.561410i	1.42065	+	1.95536i	1.46939	−	3.30030i	10.7916	+	9.71676i	−20.3872	−	6.62419i	2.66646	−	25.3696i	3.57584	−	6.19354i
4.13	−1.03639	−	2.32777i	5.56892	+	6.18492i	1.00863	−	1.12020i	−8.42071	−	11.5901i	8.62549	−	19.3732i	−19.8479	−	17.8711i	−23.0397	−	7.48606i	−4.41801	+	42.0346i	−18.2520	+	31.6134i
4.14	−0.932085	−	2.09350i	−2.70985	−	3.00960i	1.83910	−	2.04253i	9.72349	+	13.3832i	−3.77477	+	8.47826i	−15.0677	−	13.5670i	−23.4259	−	7.61153i	1.10790	−	10.5410i	18.9546	−	32.8304i
4.15	−0.808147	−	1.81513i	−3.79496	−	4.21473i	2.71146	−	3.01138i	0.524398	+	0.721772i	−4.58340	+	10.2945i	−6.62443	−	5.96466i	−22.7746	−	7.39990i	−0.539967	+	5.13745i	0.886318	−	1.53515i
4.16	−0.575206	−	1.29193i	2.66712	+	2.96213i	4.01481	−	4.45890i	3.01771	+	4.15352i	2.29274	−	5.14957i	−20.4877	−	18.4472i	−18.8298	−	6.11817i	1.16155	−	11.0514i	3.63027	−	6.28781i
4.17	−0.422353	−	0.948621i	2.15968	+	2.39857i	4.63155	−	5.14385i	−5.52326	−	7.60212i	1.36318	−	3.06176i	−2.74382	−	2.47055i	−14.7363	−	4.78811i	1.73336	−	16.4918i	−4.87876	+	8.45026i
4.18	−0.283822	−	0.637475i	1.45489	+	1.61582i	5.02723	−	5.58330i	8.75512	+	12.0504i	0.617114	−	1.38606i	8.49041	+	7.64480i	−10.2953	−	3.34513i	2.32810	−	22.1504i	5.19693	−	9.00135i
4.19	−0.128739	−	0.289154i	−4.76114	−	5.28778i	5.28601	−	5.87071i	−8.56936	−	11.7947i	−0.916034	+	2.05745i	−15.6398	−	14.0822i	−4.78627	−	1.55515i	−2.46991	+	23.4996i	−2.30727	+	3.99630i
4.20	−0.0296548	−	0.0666058i	5.09912	+	5.66315i	5.34949	−	5.94121i	−7.83131	−	10.7789i	0.225985	−	0.507571i	23.1390	+	20.8345i	−1.10908	−	0.360363i	−3.24794	+	30.9021i	−0.485699	+	0.841256i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.c	even	5	1	inner
13.e	even	6	1	inner
143.u	even	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.4.u.a	✓	320
11.c	even	5	1	inner	143.4.u.a	✓	320
13.e	even	6	1	inner	143.4.u.a	✓	320
143.u	even	30	1	inner	143.4.u.a	✓	320

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.4.u.a	✓	320	1.a	even	1	1	trivial
143.4.u.a	✓	320	11.c	even	5	1	inner
143.4.u.a	✓	320	13.e	even	6	1	inner
143.4.u.a	✓	320	143.u	even	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(143, [\chi])\).