Newform orbit 143.3.k.a

• Label: 143.3.k.a
• Level: $143$
• Weight: $3$
• Character orbit: 143.k
• Analytic conductor: $3.896$
• Analytic rank: $0$
• Dimension: $52$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	143.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.89646778035\)
Analytic rank:	\(0\)
Dimension:	\(52\)
Relative dimension:	\(26\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52 q - 2 q^{3} + 46 q^{4} - 8 q^{5} - 64 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
87.1	−3.24138	−	1.87141i	−1.02066	+	1.76784i	5.00438	+	8.66783i	−7.74383			6.61672	−	3.82016i	−8.33645	+	4.81305i		−	22.4897i	2.41649	+	4.18549i	25.1007	+	14.4919i
87.2	−3.16880	−	1.82951i	2.29405	−	3.97341i	4.69421	+	8.13062i	0.250330			−14.5388	+	8.39396i	9.27430	−	5.35452i		−	19.7164i	−6.02531	−	10.4361i	−0.793247	−	0.457981i
87.3	−2.76501	−	1.59638i	−2.65361	+	4.59619i	3.09686	+	5.36392i	7.93481			14.6745	−	8.47234i	−3.69626	+	2.13404i		−	7.00403i	−9.58329	−	16.5987i	−21.9398	−	12.6670i
87.4	−2.75175	−	1.58872i	0.495510	−	0.858248i	3.04808	+	5.27942i	1.84523			−2.72704	+	1.57445i	−1.05318	+	0.608052i		−	6.66040i	4.00894	+	6.94369i	−5.07760	−	2.93156i
87.5	−2.64275	−	1.52579i	−1.48872	+	2.57854i	2.65608	+	4.60047i	−1.44788			7.86862	−	4.54295i	7.81786	−	4.51364i		−	4.00418i	0.0674375	+	0.116805i	3.82638	+	2.20916i
87.6	−2.27241	−	1.31198i	2.07037	−	3.58599i	1.44257	+	2.49860i	−3.46133			−9.40947	+	5.43256i	−6.69553	+	3.86567i			2.92534i	−4.07287	−	7.05441i	7.86557	+	4.54119i
87.7	−1.76865	−	1.02113i	−0.0926289	+	0.160438i	0.0854156	+	0.147944i	5.99203			0.327656	−	0.189173i	0.186167	−	0.107483i			7.82016i	4.48284	+	7.76451i	−10.5978	−	6.11864i
87.8	−1.20286	−	0.694474i	−0.232350	+	0.402442i	−1.03541	−	1.79339i	−8.38579			0.558971	−	0.322722i	6.41342	−	3.70279i			8.43206i	4.39203	+	7.60721i	10.0870	+	5.82371i
87.9	−1.10445	−	0.637652i	−2.48604	+	4.30594i	−1.18680	−	2.05560i	−3.62517			5.49138	−	3.17045i	1.99125	−	1.14965i			8.12828i	−7.86075	−	13.6152i	4.00380	+	2.31160i
87.10	−1.01194	−	0.584243i	1.93953	−	3.35937i	−1.31732	−	2.28166i	7.51869			−3.92538	+	2.26632i	6.54691	−	3.77986i			7.75249i	−3.02358	−	5.23700i	−7.60845	−	4.39274i
87.11	−0.965319	−	0.557327i	0.0513447	−	0.0889316i	−1.37877	−	2.38811i	−1.68627			−0.0991279	+	0.0572315i	−8.39396	+	4.84625i			7.53233i	4.49473	+	7.78510i	1.62779	+	0.939805i
87.12	−0.652932	−	0.376970i	2.17629	−	3.76945i	−1.71579	−	2.97183i	−3.74617			−2.84194	+	1.64079i	3.93998	−	2.27475i			5.60297i	−4.97249	−	8.61260i	2.44599	+	1.41220i
87.13	−0.399685	−	0.230758i	−1.55309	+	2.69003i	−1.89350	−	3.27964i	4.55537			1.24149	−	0.716777i	−7.58582	+	4.37968i			3.59383i	−0.324189	−	0.561511i	−1.82071	−	1.05119i
87.14	0.399685	+	0.230758i	−1.55309	+	2.69003i	−1.89350	−	3.27964i	4.55537			−1.24149	+	0.716777i	7.58582	−	4.37968i		−	3.59383i	−0.324189	−	0.561511i	1.82071	+	1.05119i
87.15	0.652932	+	0.376970i	2.17629	−	3.76945i	−1.71579	−	2.97183i	−3.74617			2.84194	−	1.64079i	−3.93998	+	2.27475i		−	5.60297i	−4.97249	−	8.61260i	−2.44599	−	1.41220i
87.16	0.965319	+	0.557327i	0.0513447	−	0.0889316i	−1.37877	−	2.38811i	−1.68627			0.0991279	−	0.0572315i	8.39396	−	4.84625i		−	7.53233i	4.49473	+	7.78510i	−1.62779	−	0.939805i
87.17	1.01194	+	0.584243i	1.93953	−	3.35937i	−1.31732	−	2.28166i	7.51869			3.92538	−	2.26632i	−6.54691	+	3.77986i		−	7.75249i	−3.02358	−	5.23700i	7.60845	+	4.39274i
87.18	1.10445	+	0.637652i	−2.48604	+	4.30594i	−1.18680	−	2.05560i	−3.62517			−5.49138	+	3.17045i	−1.99125	+	1.14965i		−	8.12828i	−7.86075	−	13.6152i	−4.00380	−	2.31160i
87.19	1.20286	+	0.694474i	−0.232350	+	0.402442i	−1.03541	−	1.79339i	−8.38579			−0.558971	+	0.322722i	−6.41342	+	3.70279i		−	8.43206i	4.39203	+	7.60721i	−10.0870	−	5.82371i
87.20	1.76865	+	1.02113i	−0.0926289	+	0.160438i	0.0854156	+	0.147944i	5.99203			−0.327656	+	0.189173i	−0.186167	+	0.107483i		−	7.82016i	4.48284	+	7.76451i	10.5978	+	6.11864i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
13.c	even	3	1	inner
143.k	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	143.3.k.a	✓	52
11.b	odd	2	1	inner	143.3.k.a	✓	52
13.c	even	3	1	inner	143.3.k.a	✓	52
143.k	odd	6	1	inner	143.3.k.a	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.3.k.a	✓	52	1.a	even	1	1	trivial
143.3.k.a	✓	52	11.b	odd	2	1	inner
143.3.k.a	✓	52	13.c	even	3	1	inner
143.3.k.a	✓	52	143.k	odd	6	1	inner

Hecke kernels

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