Newform orbit 144.4.u.a

• Label: 144.4.u.a
• Level: $144$
• Weight: $4$
• Character orbit: 144.u
• Analytic conductor: $8.496$
• Analytic rank: $0$
• Dimension: $280$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.u (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.49627504083\)
Analytic rank:	\(0\)
Dimension:	\(280\)
Relative dimension:	\(70\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 280 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 34 q^{6} - 4 q^{7}+O(q^{10}) \)

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	−2.82298	−	0.175485i	5.17711	+	0.444425i	7.93841	+	0.990780i	9.81688	+	2.63042i	−14.5369	−	2.16311i	15.2172	−	26.3570i	−22.2361	−	4.19002i	26.6050	+	4.60168i	−27.2512	−	9.14834i
11.2	−2.82047	+	0.212015i	2.11466	−	4.74639i	7.91010	−	1.19596i	−9.26698	−	2.48308i	−4.95803	+	13.8354i	1.44281	−	2.49902i	−22.0566	+	5.05023i	−18.0564	−	20.0740i	26.6637	+	5.03871i
11.3	−2.81806	−	0.241890i	0.864807	+	5.12368i	7.88298	+	1.36332i	1.77078	+	0.474479i	−1.19772	−	14.6481i	−15.7482	+	27.2767i	−21.8850	−	5.74875i	−25.5042	+	8.86199i	−4.87540	−	1.76545i
11.4	−2.80616	−	0.354211i	−5.19548	−	0.0837906i	7.74907	+	1.98795i	−13.7230	−	3.67706i	14.5497	+	2.07543i	−11.1409	+	19.2966i	−21.0410	−	8.32331i	26.9860	+	0.870664i	37.2064	+	15.1793i
11.5	−2.79559	−	0.429718i	−4.23000	+	3.01779i	7.63069	+	2.40263i	20.7935	+	5.57161i	13.1222	−	6.61882i	1.74853	−	3.02854i	−20.2998	−	9.99582i	8.78583	−	25.5306i	−55.7360	−	24.5113i
11.6	−2.78134	−	0.513936i	−3.56319	−	3.78202i	7.47174	+	2.85887i	−0.0665396	−	0.0178292i	7.96673	+	12.3504i	11.6771	−	20.2253i	−19.3122	−	11.7915i	−1.60739	+	26.9521i	0.175906	+	0.0837863i
11.7	−2.65670	+	0.970533i	5.19295	−	0.182480i	6.11613	−	5.15683i	12.3606	+	3.31201i	−13.6190	+	5.52472i	−16.2528	+	28.1507i	−11.2439	+	19.6361i	26.9334	−	1.89522i	−36.0528	+	3.19734i
11.8	−2.64277	+	1.00786i	4.64884	+	2.32126i	5.96844	−	5.32707i	−19.9615	−	5.34866i	−14.6253	−	1.44918i	3.97013	−	6.87647i	−10.4043	+	20.0936i	16.2235	+	21.5824i	58.1442	−	5.98307i
11.9	−2.60967	+	1.09071i	−0.264879	+	5.18940i	5.62072	−	5.69276i	0.193919	+	0.0519604i	−4.96886	−	13.8315i	6.92045	−	11.9866i	−8.45906	+	20.9868i	−26.8597	−	2.74912i	−0.562737	+	0.0759093i
11.10	−2.58743	+	1.14245i	−2.96659	−	4.26607i	5.38961	−	5.91203i	5.94311	+	1.59245i	12.5496	+	7.64899i	−6.07158	+	10.5163i	−7.19105	+	21.4543i	−9.39873	+	25.3113i	−17.1967	+	2.66935i
11.11	−2.51243	−	1.29911i	−1.89133	+	4.83972i	4.62460	+	6.52787i	−11.6142	−	3.11201i	11.0392	−	9.70240i	10.4169	−	18.0426i	−3.13855	−	22.4087i	−19.8458	−	18.3070i	25.1369	+	22.9068i
11.12	−2.50474	−	1.31387i	−1.14146	−	5.06923i	4.54749	+	6.58182i	15.4744	+	4.14636i	−3.80126	+	14.1968i	−10.2797	+	17.8050i	−2.74264	−	22.4606i	−24.3942	+	11.5726i	−33.3117	−	30.7170i
11.13	−2.43297	+	1.44245i	−5.00684	+	1.38979i	3.83867	−	7.01888i	1.18962	+	0.318757i	10.1768	−	10.6034i	0.560791	−	0.971319i	0.785023	+	22.6138i	23.1370	−	13.9169i	−3.35410	+	0.940440i
11.14	−2.40927	−	1.48169i	4.33732	+	2.86141i	3.60920	+	7.13959i	−10.2226	−	2.73913i	−6.21006	−	13.3205i	−3.41459	+	5.91424i	1.88310	−	22.5489i	10.6246	+	24.8217i	20.5705	+	21.7460i
11.15	−2.36396	−	1.55297i	4.32647	−	2.87778i	3.17660	+	7.34229i	2.85215	+	0.764232i	−14.6967	+	0.0840952i	−3.28622	+	5.69190i	3.89298	−	22.2900i	10.4367	−	24.9013i	−5.55555	−	6.23591i
11.16	−2.09176	+	1.90382i	1.45622	−	4.98793i	0.750922	−	7.96468i	17.8590	+	4.78530i	6.45006	+	13.2059i	14.4830	−	25.0853i	13.5926	+	18.0898i	−22.7588	−	14.5270i	−46.4670	+	23.9906i
11.17	−1.96374	−	2.03562i	−5.17650	−	0.451512i	−0.287477	+	7.99483i	2.08007	+	0.557352i	9.24617	+	11.4240i	10.2879	−	17.8191i	16.8390	−	15.1146i	26.5923	+	4.67451i	−2.95015	−	5.32871i
11.18	−1.91060	+	2.08557i	4.00742	−	3.30765i	−0.699212	−	7.96939i	−6.66877	−	1.78689i	−0.758240	+	14.6774i	−4.54494	+	7.87207i	17.9566	+	13.7681i	5.11887	−	26.5103i	16.4680	−	10.4942i
11.19	−1.85857	−	2.13207i	−1.25634	−	5.04199i	−1.09141	+	7.92520i	−20.8053	−	5.57475i	−8.41485	+	12.0495i	−8.02552	+	13.9006i	18.9255	−	12.4026i	−23.8432	+	12.6689i	26.7824	+	54.7193i
11.20	−1.82364	−	2.16202i	2.61106	+	4.49248i	−1.34866	+	7.88550i	16.7996	+	4.50145i	4.95119	−	13.8378i	3.33703	−	5.77991i	19.5081	−	11.4645i	−13.3647	+	23.4603i	−20.9043	−	44.5302i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.d	odd	6	1	inner
16.f	odd	4	1	inner
144.u	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	144.4.u.a	✓	280
9.d	odd	6	1	inner	144.4.u.a	✓	280
16.f	odd	4	1	inner	144.4.u.a	✓	280
144.u	even	12	1	inner	144.4.u.a	✓	280

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.4.u.a	✓	280	1.a	even	1	1	trivial
144.4.u.a	✓	280	9.d	odd	6	1	inner
144.4.u.a	✓	280	16.f	odd	4	1	inner
144.4.u.a	✓	280	144.u	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(144, [\chi])\).