Newform orbit 144.3.w.a

• Label: 144.3.w.a
• Level: $144$
• Weight: $3$
• Character orbit: 144.w
• Analytic conductor: $3.924$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(3.92371580679\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(46\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−1.99959	+	0.0402970i	0.538615	+	2.95125i	3.99675	−	0.161155i	−2.08673	−	7.78777i	−1.19594	−	5.87960i	−2.60739	+	1.50538i	−7.98539	+	0.483303i	−8.41979	+	3.17918i	4.48643	+	15.4883i
5.2	−1.99458	+	0.147176i	−2.86084	+	0.903108i	3.95668	−	0.587107i	−0.0992523	−	0.370415i	5.57325	−	2.22237i	3.11010	−	1.79562i	−7.80549	+	1.75336i	7.36879	−	5.16729i	0.252482	+	0.724213i
5.3	−1.98351	+	0.256277i	−1.40595	−	2.65015i	3.86864	−	1.01666i	1.00259	+	3.74171i	3.46789	+	4.89630i	4.65369	−	2.68681i	−7.41296	+	3.00800i	−5.04662	+	7.45195i	−2.94756	−	7.16478i
5.4	−1.88582	−	0.666085i	2.99994	+	0.0192045i	3.11266	+	2.51224i	−0.345472	−	1.28932i	−5.64456	−	2.03443i	4.11923	−	2.37824i	−4.19657	−	6.81093i	8.99926	+	0.115225i	−0.207297	+	2.66154i
5.5	−1.88357	+	0.672432i	2.93495	+	0.621365i	3.09567	−	2.53315i	1.03307	+	3.85549i	−5.94600	+	0.803167i	−11.2715	+	6.50760i	−4.12754	+	6.85298i	8.22781	+	3.64735i	−4.53842	−	6.56740i
5.6	−1.84760	−	0.765753i	−0.120474	+	2.99758i	2.82724	+	2.82961i	2.37709	+	8.87143i	2.51799	−	5.44607i	0.152137	−	0.0878365i	−3.05683	−	7.39295i	−8.97097	−	0.722263i	2.40141	−	18.2111i
5.7	−1.79350	−	0.885072i	0.352522	−	2.97922i	2.43329	+	3.17476i	0.899691	+	3.35769i	−3.26907	+	5.03122i	−9.56176	+	5.52049i	−1.55423	−	7.84757i	−8.75146	−	2.10048i	1.35820	−	6.81832i
5.8	−1.73513	+	0.994646i	1.85623	−	2.35678i	2.02136	−	3.45168i	−0.777454	−	2.90150i	−0.876653	+	5.93561i	2.72697	−	1.57442i	−0.0741259	+	7.99966i	−2.10879	−	8.74946i	4.23494	+	4.26119i
5.9	−1.61016	−	1.18633i	−2.90827	+	0.736170i	1.18523	+	3.82037i	−0.295811	−	1.10398i	5.55613	+	2.26483i	−7.30360	+	4.21674i	2.62382	−	7.55748i	7.91611	−	4.28197i	−0.833388	+	2.12852i
5.10	−1.59704	−	1.20393i	−1.75135	−	2.43573i	1.10109	+	3.84547i	−2.49590	−	9.31484i	−0.135487	+	5.99847i	7.55275	−	4.36058i	2.87120	−	7.46701i	−2.86558	+	8.53161i	−7.22838	+	17.8811i
5.11	−1.58134	+	1.22449i	1.74774	+	2.43832i	1.00126	−	3.87266i	0.973349	+	3.63259i	−5.74946	−	1.71573i	11.7048	−	6.75777i	3.15868	+	7.35002i	−2.89081	+	8.52310i	−5.98725	−	4.55250i
5.12	−1.51447	+	1.30628i	−2.22089	−	2.01684i	0.587245	−	3.95666i	−1.88738	−	7.04379i	5.99804	+	0.153334i	−8.89672	+	5.13652i	4.27915	+	6.75935i	0.864706	+	8.95836i	12.0596	+	8.20216i
5.13	−1.26432	+	1.54968i	−2.98386	−	0.310733i	−0.803013	−	3.91857i	2.23236	+	8.33129i	4.25408	−	4.23117i	−3.69610	+	2.13394i	7.08778	+	3.70989i	8.80689	+	1.85437i	−15.7332	−	7.07393i
5.14	−1.16958	+	1.62237i	−1.89172	+	2.32839i	−1.26417	−	3.79498i	−1.06962	−	3.99189i	−1.56500	−	5.79230i	2.82785	−	1.63266i	7.63541	+	2.38759i	−1.84282	−	8.80931i	7.72733	+	2.93351i
5.15	−1.09867	−	1.67120i	0.894041	+	2.86368i	−1.58584	+	3.67221i	−0.835695	−	3.11886i	3.80354	−	4.64037i	0.108974	−	0.0629164i	7.87933	−	1.38428i	−7.40138	+	5.12050i	−4.29409	+	4.82321i
5.16	−1.08605	−	1.67944i	1.99667	−	2.23905i	−1.64101	+	3.64789i	1.20857	+	4.51043i	−5.92880	−	0.921569i	7.69955	−	4.44534i	7.90861	−	1.20579i	−1.02665	−	8.94125i	6.26242	−	6.92824i
5.17	−0.786053	+	1.83905i	1.51963	−	2.58664i	−2.76424	−	2.89119i	1.99100	+	7.43050i	3.56247	+	4.82792i	−1.50577	+	0.869355i	7.48989	−	2.81097i	−4.38144	−	7.86149i	−15.2301	−	2.17922i
5.18	−0.762335	−	1.84901i	−2.07303	+	2.16854i	−2.83769	+	2.81913i	−0.115759	−	0.432017i	5.58999	+	2.17990i	7.23679	−	4.17816i	7.37588	+	3.09780i	−0.405106	−	8.99088i	−0.710557	+	0.543380i
5.19	−0.702398	+	1.87260i	1.41045	+	2.64776i	−3.01327	−	2.63062i	−0.226081	−	0.843746i	−5.94890	+	0.781440i	−7.54519	+	4.35622i	7.04263	−	3.79492i	−5.02124	+	7.46908i	1.73880	+	0.169286i
5.20	−0.608739	−	1.90511i	2.61769	−	1.46550i	−3.25887	+	2.31943i	−2.13498	−	7.96785i	−4.38543	−	4.09487i	−10.2471	+	5.91616i	6.40256	+	4.79658i	4.70460	−	7.67247i	−13.8800	+	8.91771i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	144.3.w.a	✓	184
3.b	odd	2	1		432.3.x.a		184
9.c	even	3	1		432.3.x.a		184
9.d	odd	6	1	inner	144.3.w.a	✓	184
16.e	even	4	1	inner	144.3.w.a	✓	184
48.i	odd	4	1		432.3.x.a		184
144.w	odd	12	1	inner	144.3.w.a	✓	184
144.x	even	12	1		432.3.x.a		184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.3.w.a	✓	184	1.a	even	1	1	trivial
144.3.w.a	✓	184	9.d	odd	6	1	inner
144.3.w.a	✓	184	16.e	even	4	1	inner
144.3.w.a	✓	184	144.w	odd	12	1	inner
432.3.x.a		184	3.b	odd	2	1
432.3.x.a		184	9.c	even	3	1
432.3.x.a		184	48.i	odd	4	1
432.3.x.a		184	144.x	even	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(144, [\chi])\).