Newform orbit 135.3.o.a

• Label: 135.3.o.a
• Level: $135$
• Weight: $3$
• Character orbit: 135.o
• Analytic conductor: $3.678$
• Analytic rank: $0$
• Dimension: $144$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.o (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.67848356886\)
Analytic rank:	\(0\)
Dimension:	\(144\)
Relative dimension:	\(24\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 144 q + 12 q^{6} - 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−2.42881	+	2.89455i	−0.324060	+	2.98245i	−1.78467	−	10.1214i	−0.764780	+	2.10122i	−7.84575	−	8.18181i	1.87051	−	10.6082i	20.5422	+	11.8600i	−8.78997	−	1.93298i	−4.22456	−	7.31715i
11.2	−2.34453	+	2.79411i	2.98485	+	0.301114i	−1.61560	−	9.16252i	0.764780	−	2.10122i	−7.83942	+	7.63402i	0.433594	−	2.45903i	16.7538	+	9.67278i	8.81866	+	1.79756i	4.07797	+	7.06325i
11.3	−2.25031	+	2.68181i	0.287591	−	2.98618i	−1.43364	−	8.13057i	−0.764780	+	2.10122i	7.36121	+	7.49110i	0.0660262	−	0.374453i	12.9035	+	7.44982i	−8.83458	−	1.71760i	−3.91408	−	6.77938i
11.4	−1.78728	+	2.12999i	0.615724	+	2.93613i	−0.647921	−	3.67454i	0.764780	−	2.10122i	−7.35442	−	3.93620i	−1.68672	+	9.56586i	−0.647200	−	0.373661i	−8.24177	+	3.61570i	3.10870	+	5.38443i
11.5	−1.77403	+	2.11421i	1.04716	−	2.81131i	−0.628101	−	3.56214i	0.764780	−	2.10122i	4.08600	+	7.20128i	−0.591008	+	3.35177i	−0.915208	−	0.528396i	−6.80691	−	5.88779i	3.08567	+	5.34454i
11.6	−1.66807	+	1.98793i	−2.63089	+	1.44168i	−0.474813	−	2.69280i	0.764780	−	2.10122i	1.52256	−	7.63485i	1.62354	−	9.20757i	−2.84443	−	1.64223i	4.84314	−	7.58578i	2.90137	+	5.02531i
11.7	−1.42827	+	1.70214i	2.36415	+	1.84683i	−0.162750	−	0.923000i	−0.764780	+	2.10122i	−6.52021	+	1.38635i	−0.471254	+	2.67261i	−5.89367	−	3.40271i	2.17841	+	8.73238i	−2.48426	−	4.30286i
11.8	−1.31412	+	1.56611i	−2.14460	−	2.09778i	−0.0311872	−	0.176872i	−0.764780	+	2.10122i	6.10361	−	0.601947i	1.09079	−	6.18616i	−6.76405	−	3.90523i	0.198653	+	8.99781i	−2.28572	−	3.95898i
11.9	−0.783627	+	0.933890i	−2.03941	−	2.20018i	0.436513	+	2.47559i	0.764780	−	2.10122i	3.65286	−	0.180463i	−0.509205	+	2.88785i	−6.87710	−	3.97050i	−0.681608	+	8.97415i	1.36300	+	2.36079i
11.10	−0.473737	+	0.564578i	−2.51003	+	1.64310i	0.600271	+	3.40431i	−0.764780	+	2.10122i	0.261437	−	2.19550i	−0.393427	+	2.23123i	−4.75943	−	2.74786i	3.60047	−	8.24843i	−0.823996	−	1.42720i
11.11	−0.423305	+	0.504475i	1.84516	−	2.36546i	0.619285	+	3.51214i	−0.764780	+	2.10122i	0.412249	+	1.93215i	−2.33662	+	13.2516i	−4.31520	−	2.49138i	−2.19077	−	8.72929i	−0.736276	−	1.27527i
11.12	0.0486755	−	0.0580092i	2.87760	+	0.848196i	0.693597	+	3.93358i	0.764780	−	2.10122i	0.189272	−	0.125641i	−0.688197	+	3.90296i	0.524266	+	0.302685i	7.56113	+	4.88153i	−0.0846638	−	0.146642i
11.13	0.194448	−	0.231735i	1.14017	−	2.77489i	0.678702	+	3.84911i	0.764780	−	2.10122i	−0.421334	−	0.803790i	1.88885	−	10.7122i	2.07186	+	1.19619i	−6.40003	−	6.32769i	−0.338214	−	0.585804i
11.14	0.409641	−	0.488191i	1.19696	+	2.75087i	0.624068	+	3.53926i	−0.764780	+	2.10122i	1.83328	+	0.542524i	1.70919	−	9.69329i	4.19111	+	2.41974i	−6.13457	+	6.58536i	0.712510	+	1.23410i
11.15	0.815617	−	0.972015i	−2.84865	−	0.940848i	0.415011	+	2.35365i	−0.764780	+	2.10122i	−3.23793	+	2.00156i	−0.201664	+	1.14369i	7.02178	+	4.05403i	7.22961	+	5.36029i	1.41865	+	2.45717i
11.16	0.907414	−	1.08141i	−2.99927	−	0.0663157i	0.348537	+	1.97665i	0.764780	−	2.10122i	−2.79329	+	3.18327i	1.93462	−	10.9718i	7.34407	+	4.24010i	8.99120	+	0.397797i	−1.57831	−	2.73372i
11.17	1.09359	−	1.30329i	2.88912	−	0.808067i	0.191970	+	1.08871i	−0.764780	+	2.10122i	2.10637	−	4.64905i	0.637454	−	3.61518i	7.52239	+	4.34305i	7.69406	−	4.66921i	1.90213	+	3.29459i
11.18	1.18935	−	1.41741i	−2.22222	+	2.01538i	0.100087	+	0.567621i	0.764780	−	2.10122i	0.213632	+	5.54680i	−1.53470	+	8.70370i	7.33323	+	4.23384i	0.876487	−	8.95722i	−2.06870	−	3.58310i
11.19	1.46579	−	1.74686i	0.511020	+	2.95616i	−0.208383	−	1.18180i	−0.764780	+	2.10122i	5.91302	+	3.44041i	−1.98144	+	11.2373i	5.52951	+	3.19247i	−8.47772	+	3.02131i	2.54952	+	4.41589i
11.20	1.80909	−	2.15599i	1.89464	−	2.32601i	−0.680891	−	3.86152i	0.764780	−	2.10122i	−1.58729	−	8.29279i	−1.00302	+	5.68841i	0.192328	+	0.111041i	−1.82068	−	8.81392i	−3.14664	−	5.45015i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
27.f	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	135.3.o.a	✓	144
3.b	odd	2	1		405.3.o.a		144
27.e	even	9	1		405.3.o.a		144
27.f	odd	18	1	inner	135.3.o.a	✓	144

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
135.3.o.a	✓	144	1.a	even	1	1	trivial
135.3.o.a	✓	144	27.f	odd	18	1	inner
405.3.o.a		144	3.b	odd	2	1
405.3.o.a		144	27.e	even	9	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(135, [\chi])\).