Newform orbit 143.3.x.a

• Label: 143.3.x.a
• Level: $143$
• Weight: $3$
• Character orbit: 143.x
• Analytic conductor: $3.896$
• Analytic rank: $0$
• Dimension: $416$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	143.x (of order \(60\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.89646778035\)
Analytic rank:	\(0\)
Dimension:	\(416\)
Relative dimension:	\(26\) over \(\Q(\zeta_{60})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 416 q - 12 q^{2} - 6 q^{3} - 18 q^{4} - 12 q^{5} - 28 q^{6} - 12 q^{7} + 4 q^{8} + 126 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
15.1	−2.32625	−	2.87268i	−3.36943	+	0.716195i	−2.00921	+	9.45258i	−1.04665	+	6.60829i	9.89555	+	8.01326i	−4.33114	−	6.66936i	18.6540	−	9.50466i	2.61823	−	1.16571i	21.4183	−	12.3659i
15.2	−2.30707	−	2.84900i	−2.29818	+	0.488494i	−1.96256	+	9.23311i	0.820972	−	5.18342i	6.69379	+	5.42053i	6.63766	+	10.2211i	17.7672	−	9.05286i	−3.17889	+	1.41533i	−16.6616	+	9.61957i
15.3	−2.23118	−	2.75527i	5.15210	−	1.09511i	−1.78174	+	8.38240i	−1.24740	+	7.87576i	−14.5126	−	11.7520i	1.40858	+	2.16903i	14.4354	−	7.35519i	17.1229	−	7.62362i	24.4830	−	14.1353i
15.4	−2.00444	−	2.47527i	1.26393	−	0.268657i	−1.27756	+	6.01046i	0.107818	−	0.680737i	−3.19847	−	2.59007i	−2.16442	−	3.33292i	6.08659	−	3.10128i	−6.69656	+	2.98150i	−1.90112	+	1.09761i
15.5	−1.72816	−	2.13410i	4.29634	−	0.913216i	−0.736192	+	3.46351i	1.15494	−	7.29200i	−9.37364	−	7.59062i	2.16355	+	3.33158i	−1.12334	+	0.572373i	9.40268	−	4.18634i	−17.5577	+	10.1370i
15.6	−1.58502	−	1.95733i	−4.81165	+	1.02275i	−0.487229	+	2.29223i	1.37420	−	8.67637i	9.62842	+	7.79694i	−5.98498	−	9.21606i	−3.71749	+	1.89416i	13.8841	−	6.18159i	−19.1607	+	11.0624i
15.7	−1.54727	−	1.91072i	−1.40193	+	0.297989i	−0.425165	+	2.00024i	−0.194031	+	1.22506i	2.73854	+	2.21762i	−0.619325	−	0.953677i	−4.28291	+	2.18225i	−6.34531	+	2.82511i	2.64097	−	1.52477i
15.8	−1.33739	−	1.65154i	1.01179	−	0.215062i	−0.107320	+	0.504903i	−0.928523	+	5.86247i	−1.70833	−	1.38338i	5.59682	+	8.61835i	−6.59663	+	3.36115i	−7.24445	+	3.22544i	10.9239	−	6.30690i
15.9	−1.03738	−	1.28106i	3.02155	−	0.642250i	0.266698	−	1.25471i	−0.0624081	+	0.394029i	−3.95725	−	3.20452i	−6.65322	−	10.2451i	−7.75900	+	3.95341i	0.495372	−	0.220554i	0.569514	−	0.328809i
15.10	−0.901785	−	1.11361i	−4.82609	+	1.02582i	0.404732	−	1.90411i	−0.855758	+	5.40304i	5.49446	+	4.44933i	0.898384	+	1.38339i	−7.59250	+	3.86857i	14.0170	−	6.24075i	6.78860	−	3.91940i
15.11	−0.634076	−	0.783019i	−2.74209	+	0.582849i	0.620581	−	2.91960i	0.688364	−	4.34616i	2.19507	+	1.77754i	2.22937	+	3.43293i	−6.27056	+	3.19501i	−1.04257	+	0.464182i	−3.83960	+	2.21679i
15.12	−0.455608	−	0.562629i	1.72143	−	0.365902i	0.722674	−	3.39991i	1.32469	−	8.36377i	−0.990165	−	0.801820i	1.29304	+	1.99110i	−4.82238	+	2.45713i	−5.39246	+	2.40088i	−5.30923	+	3.06529i
15.13	−0.197927	−	0.244419i	5.51004	−	1.17119i	0.811081	−	3.81584i	−0.316909	+	2.00089i	−1.37685	−	1.11495i	−0.829205	−	1.27686i	−2.21412	+	1.12815i	20.7669	−	9.24602i	0.551780	−	0.318570i
15.14	−0.0330410	−	0.0408022i	−2.28061	+	0.484758i	0.831074	−	3.90989i	−0.708282	+	4.47192i	0.0951328	+	0.0770370i	−3.34268	−	5.14728i	−0.374113	+	0.190620i	−3.25572	+	1.44954i	0.205867	−	0.118857i
15.15	0.155357	+	0.191850i	3.01364	−	0.640570i	0.818976	−	3.85298i	−0.234160	+	1.47843i	0.591086	+	0.478652i	5.96535	+	9.18584i	1.74626	−	0.889766i	0.449812	−	0.200269i	−0.320015	+	0.184761i
15.16	0.584280	+	0.721526i	−0.197077	+	0.0418900i	0.652430	−	3.06944i	0.391863	−	2.47413i	−0.145373	−	0.117721i	−5.04086	−	7.76225i	5.90484	−	3.00866i	−8.18482	+	3.64412i	2.01410	−	1.16284i
15.17	0.631628	+	0.779996i	−4.72698	+	1.00475i	0.622207	−	2.92726i	0.298225	−	1.88292i	−3.76940	−	3.05240i	6.21428	+	9.56915i	6.25335	−	3.18624i	13.1129	−	5.83824i	1.65704	−	0.956691i
15.18	0.794977	+	0.981715i	−0.472113	+	0.100351i	0.499871	−	2.35171i	−1.45627	+	9.19455i	−0.473835	−	0.383704i	1.25181	+	1.92761i	7.20828	−	3.67280i	−8.00909	+	3.56588i	−10.1841	+	5.87982i
15.19	1.18503	+	1.46339i	3.22906	−	0.686357i	0.0944359	−	0.444286i	0.243108	−	1.53492i	4.83092	+	3.91200i	−1.51394	−	2.33126i	7.47323	−	3.80780i	1.73380	−	0.771939i	2.53427	−	1.46316i
15.20	1.31081	+	1.61872i	−3.50993	+	0.746058i	−0.0703772	+	0.331099i	1.03607	−	6.54148i	−5.80853	−	4.70365i	−1.94462	−	2.99445i	6.79532	−	3.46239i	3.54109	−	1.57659i	11.9469	−	6.89756i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.c	even	5	1	inner
13.f	odd	12	1	inner
143.x	odd	60	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.3.x.a	✓	416
11.c	even	5	1	inner	143.3.x.a	✓	416
13.f	odd	12	1	inner	143.3.x.a	✓	416
143.x	odd	60	1	inner	143.3.x.a	✓	416

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.3.x.a	✓	416	1.a	even	1	1	trivial
143.3.x.a	✓	416	11.c	even	5	1	inner
143.3.x.a	✓	416	13.f	odd	12	1	inner
143.3.x.a	✓	416	143.x	odd	60	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(143, [\chi])\).