Newform orbit 143.2.o.a

• Label: 143.2.o.a
• Level: $143$
• Weight: $2$
• Character orbit: 143.o
• Analytic conductor: $1.142$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.o (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.14186074890\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 20 q^{9}+O(q^{10}) \)

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	−2.34634	+	0.628699i	−0.769085	+	1.33209i	3.37798	−	1.95028i	0.588265	−	0.588265i	0.967046	−	3.60906i	3.55603	+	0.952834i	−3.26447	+	3.26447i	0.317017	+	0.549089i	−1.01043	+	1.75011i
32.2	−2.13109	+	0.571023i	0.785846	−	1.36113i	2.48341	−	1.43380i	−2.51782	+	2.51782i	−0.897472	+	3.34941i	1.32280	+	0.354444i	−1.35350	+	1.35350i	0.264891	+	0.458805i	3.92796	−	6.80343i
32.3	−1.33681	+	0.358198i	−1.38238	+	2.39435i	−0.0732863	+	0.0423119i	−0.860682	+	0.860682i	0.990331	−	3.69597i	−1.31260	−	0.351711i	2.04004	−	2.04004i	−2.32194	−	4.02173i	0.842277	−	1.45887i
32.4	−1.21538	+	0.325660i	−0.295945	+	0.512591i	−0.360960	+	0.208401i	2.66833	−	2.66833i	0.192754	−	0.719369i	−0.951645	−	0.254993i	2.15027	−	2.15027i	1.32483	+	2.29468i	−2.37406	+	4.11199i
32.5	−0.946184	+	0.253529i	1.28851	−	2.23176i	−0.901064	+	0.520229i	0.744239	−	0.744239i	−0.653350	+	2.43834i	0.916304	+	0.245523i	2.10599	−	2.10599i	−1.82052	−	3.15323i	−0.515501	+	0.892873i
32.6	−0.197202	+	0.0528401i	−0.126947	+	0.219879i	−1.69595	+	0.979160i	−1.62233	+	1.62233i	0.0134158	−	0.0500686i	−3.99689	−	1.07096i	0.571430	−	0.571430i	1.46777	+	2.54225i	0.234202	−	0.405650i
32.7	0.197202	−	0.0528401i	−0.126947	+	0.219879i	−1.69595	+	0.979160i	−1.62233	+	1.62233i	−0.0134158	+	0.0500686i	3.99689	+	1.07096i	−0.571430	+	0.571430i	1.46777	+	2.54225i	−0.234202	+	0.405650i
32.8	0.946184	−	0.253529i	1.28851	−	2.23176i	−0.901064	+	0.520229i	0.744239	−	0.744239i	0.653350	−	2.43834i	−0.916304	−	0.245523i	−2.10599	+	2.10599i	−1.82052	−	3.15323i	0.515501	−	0.892873i
32.9	1.21538	−	0.325660i	−0.295945	+	0.512591i	−0.360960	+	0.208401i	2.66833	−	2.66833i	−0.192754	+	0.719369i	0.951645	+	0.254993i	−2.15027	+	2.15027i	1.32483	+	2.29468i	2.37406	−	4.11199i
32.10	1.33681	−	0.358198i	−1.38238	+	2.39435i	−0.0732863	+	0.0423119i	−0.860682	+	0.860682i	−0.990331	+	3.69597i	1.31260	+	0.351711i	−2.04004	+	2.04004i	−2.32194	−	4.02173i	−0.842277	+	1.45887i
32.11	2.13109	−	0.571023i	0.785846	−	1.36113i	2.48341	−	1.43380i	−2.51782	+	2.51782i	0.897472	−	3.34941i	−1.32280	−	0.354444i	1.35350	−	1.35350i	0.264891	+	0.458805i	−3.92796	+	6.80343i
32.12	2.34634	−	0.628699i	−0.769085	+	1.33209i	3.37798	−	1.95028i	0.588265	−	0.588265i	−0.967046	+	3.60906i	−3.55603	−	0.952834i	3.26447	−	3.26447i	0.317017	+	0.549089i	1.01043	−	1.75011i
54.1	−0.655158	+	2.44508i	1.51470	+	2.62354i	−3.81716	−	2.20384i	1.00655	−	1.00655i	−7.40715	+	1.98474i	0.0740200	+	0.276246i	4.30955	−	4.30955i	−3.08865	+	5.34969i	1.80164	+	3.12054i
54.2	−0.595858	+	2.22377i	−0.919692	−	1.59295i	−2.85807	−	1.65011i	1.76104	−	1.76104i	4.09037	−	1.09601i	−1.13738	−	4.24476i	2.11663	−	2.11663i	−0.191668	+	0.331979i	2.86682	+	4.96548i
54.3	−0.434323	+	1.62091i	−1.48314	−	2.56887i	−0.706676	−	0.408000i	−2.16789	+	2.16789i	4.80807	−	1.28832i	0.693856	+	2.58950i	−1.40493	+	1.40493i	−2.89939	+	5.02189i	−2.57240	−	4.45553i
54.4	−0.428977	+	1.60096i	0.382787	+	0.663007i	−0.647013	−	0.373553i	−0.104349	+	0.104349i	−1.22566	+	0.328414i	0.542295	+	2.02387i	−1.46838	+	1.46838i	1.20695	−	2.09049i	−0.122295	−	0.211822i
54.5	−0.297507	+	1.11031i	0.754212	+	1.30633i	0.587770	+	0.339349i	−2.21820	+	2.21820i	−1.67482	+	0.448767i	−0.666939	−	2.48905i	−2.17726	+	2.17726i	0.362328	−	0.627570i	−1.80296	−	3.12282i
54.6	−0.0967587	+	0.361108i	−0.748873	−	1.29709i	1.61101	+	0.930119i	0.722851	−	0.722851i	0.540849	−	0.144920i	−0.376964	−	1.40685i	−1.02045	+	1.02045i	0.378377	−	0.655369i	0.191086	+	0.330970i
54.7	0.0967587	−	0.361108i	−0.748873	−	1.29709i	1.61101	+	0.930119i	0.722851	−	0.722851i	−0.540849	+	0.144920i	0.376964	+	1.40685i	1.02045	−	1.02045i	0.378377	−	0.655369i	−0.191086	−	0.330970i
54.8	0.297507	−	1.11031i	0.754212	+	1.30633i	0.587770	+	0.339349i	−2.21820	+	2.21820i	1.67482	−	0.448767i	0.666939	+	2.48905i	2.17726	−	2.17726i	0.362328	−	0.627570i	1.80296	+	3.12282i

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	143.2.o.a	✓	48
11.b	odd	2	1	inner	143.2.o.a	✓	48
13.f	odd	12	1	inner	143.2.o.a	✓	48
143.o	even	12	1	inner	143.2.o.a	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
143.2.o.a	✓	48	1.a	even	1	1	trivial
143.2.o.a	✓	48	11.b	odd	2	1	inner
143.2.o.a	✓	48	13.f	odd	12	1	inner
143.2.o.a	✓	48	143.o	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(143, [\chi])\).