Newform orbit 143.4.o.a

• Label: 143.4.o.a
• Level: $143$
• Weight: $4$
• Character orbit: 143.o
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.o (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(40\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
32.1	−5.35695	+	1.43539i	1.66657	−	2.88658i	19.7084	−	11.3787i	−3.25582	+	3.25582i	−4.78435	+	17.8554i	5.43090	+	1.45520i	−57.8717	+	57.8717i	7.94512	+	13.7614i	12.7679	−	22.1147i
32.2	−4.87783	+	1.30701i	−4.77756	+	8.27498i	15.1567	−	8.75074i	−11.5708	+	11.5708i	12.4886	−	46.6082i	20.5354	+	5.50244i	−33.9281	+	33.9281i	−32.1502	−	55.6857i	41.3170	−	71.5632i
32.3	−4.78621	+	1.28246i	−3.24999	+	5.62914i	14.3349	−	8.27626i	13.3984	−	13.3984i	8.33597	−	31.1102i	−2.07549	−	0.556126i	−29.9659	+	29.9659i	−7.62484	−	13.2066i	−46.9448	+	81.3108i
32.4	−4.63702	+	1.24249i	−1.54154	+	2.67002i	13.0300	−	7.52287i	1.08150	−	1.08150i	3.83067	−	14.2963i	−13.7466	−	3.68339i	−23.9170	+	23.9170i	8.74733	+	15.1508i	−3.67118	+	6.35868i
32.5	−4.40813	+	1.18115i	2.35756	−	4.08341i	11.1083	−	6.41337i	2.88937	−	2.88937i	−5.56928	+	20.7848i	13.7739	+	3.69069i	−15.5758	+	15.5758i	2.38386	+	4.12898i	−9.32392	+	16.1495i
32.6	−4.16335	+	1.11557i	5.11454	−	8.85864i	9.16082	−	5.28900i	−7.67818	+	7.67818i	−11.4112	+	42.5873i	−0.565842	−	0.151617i	−7.85719	+	7.85719i	−38.8170	−	67.2330i	23.4015	−	40.5325i
32.7	−4.08019	+	1.09328i	−0.854728	+	1.48043i	8.52451	−	4.92163i	−15.4234	+	15.4234i	1.86892	−	6.97492i	−23.9363	−	6.41370i	−5.50565	+	5.50565i	12.0389	+	20.8519i	46.0684	−	79.7929i
32.8	−3.61125	+	0.967632i	3.54274	−	6.13621i	5.17664	−	2.98873i	3.98133	−	3.98133i	−6.85614	+	25.5875i	−33.6422	−	9.01441i	5.34682	−	5.34682i	−11.6020	−	20.0953i	−10.5251	+	18.2300i
32.9	−3.51428	+	0.941650i	2.24550	−	3.88932i	4.53529	−	2.61845i	14.9878	−	14.9878i	−4.22895	+	15.7827i	11.9754	+	3.20880i	7.10844	−	7.10844i	3.41546	+	5.91574i	−38.5582	+	66.7847i
32.10	−3.10849	+	0.832916i	−2.01807	+	3.49539i	2.04073	−	1.17821i	−2.38665	+	2.38665i	3.36176	−	12.5463i	25.0107	+	6.70161i	12.8423	−	12.8423i	5.35482	+	9.27482i	5.43099	−	9.40675i
32.11	−2.93374	+	0.786092i	−2.23560	+	3.87217i	1.06067	−	0.612376i	4.09175	−	4.09175i	3.51478	−	13.1173i	−10.9623	−	2.93733i	14.5508	−	14.5508i	3.50418	+	6.06942i	−8.78763	+	15.2206i
32.12	−2.78174	+	0.745366i	0.496440	−	0.859860i	0.254316	−	0.146829i	−7.62492	+	7.62492i	−0.740059	+	2.76194i	25.1138	+	6.72922i	15.6930	−	15.6930i	13.0071	+	22.5289i	15.5272	−	26.8939i
32.13	−2.64615	+	0.709034i	−4.79462	+	8.30452i	−0.428815	+	0.247577i	0.391471	−	0.391471i	6.79910	−	25.3746i	−16.3415	−	4.37870i	16.4561	−	16.4561i	−32.4767	−	56.2513i	−0.758325	+	1.31346i
32.14	−1.81132	+	0.485341i	1.94678	−	3.37192i	−3.88289	+	2.24179i	−10.0128	+	10.0128i	−1.88970	+	7.05246i	−12.3598	−	3.31179i	16.5529	−	16.5529i	5.92011	+	10.2539i	13.2767	−	22.9960i
32.15	−1.41412	+	0.378911i	1.05641	−	1.82975i	−5.07206	+	2.92835i	4.68157	−	4.68157i	−0.800569	+	2.98776i	−20.9341	−	5.60929i	14.3445	−	14.3445i	11.2680	+	19.5168i	−4.84638	+	8.39418i
32.16	−1.32670	+	0.355489i	3.59215	−	6.22179i	−5.29444	+	3.05674i	−7.26866	+	7.26866i	−2.55394	+	9.53143i	15.2517	+	4.08668i	13.7072	−	13.7072i	−12.3071	−	21.3165i	7.05942	−	12.2273i
32.17	−1.15192	+	0.308657i	−3.89437	+	6.74525i	−5.69654	+	3.28890i	12.2876	−	12.2876i	2.40405	−	8.97204i	32.4067	+	8.68335i	12.2930	−	12.2930i	−16.8323	−	29.1543i	−10.3617	+	17.9470i
32.18	−0.924432	+	0.247701i	4.37390	−	7.57581i	−6.13498	+	3.54203i	8.53113	−	8.53113i	−2.16684	+	8.08675i	20.7059	+	5.54814i	10.2079	−	10.2079i	−24.7620	−	42.8890i	−5.77328	+	9.99962i
32.19	−0.740490	+	0.198414i	−0.446262	+	0.772948i	−6.41925	+	3.70615i	7.28686	−	7.28686i	0.177089	−	0.660905i	−5.35131	−	1.43388i	8.35464	−	8.35464i	13.1017	+	22.6928i	−3.95003	+	6.84166i
32.20	−0.300514	+	0.0805224i	−3.07985	+	5.33445i	−6.84438	+	3.95160i	−9.38759	+	9.38759i	0.495993	−	1.85107i	−9.89724	−	2.65196i	3.49857	−	3.49857i	−5.47090	−	9.47587i	2.06519	−	3.57701i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
13.f	odd	12	1	inner
143.o	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.4.o.a	✓	160
11.b	odd	2	1	inner	143.4.o.a	✓	160
13.f	odd	12	1	inner	143.4.o.a	✓	160
143.o	even	12	1	inner	143.4.o.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.4.o.a	✓	160	1.a	even	1	1	trivial
143.4.o.a	✓	160	11.b	odd	2	1	inner
143.4.o.a	✓	160	13.f	odd	12	1	inner
143.4.o.a	✓	160	143.o	even	12	1	inner

Hecke kernels

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