Newform orbit 144.5.v.a

• Label: 144.5.v.a
• Level: $144$
• Weight: $5$
• Character orbit: 144.v
• Analytic conductor: $14.885$
• Analytic rank: $0$
• Dimension: $376$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.8852746841\)
Analytic rank:	\(0\)
Dimension:	\(376\)
Relative dimension:	\(94\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 376 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} - 70 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1	−3.99535	+	0.192778i	8.46055	+	3.06906i	15.9257	−	1.54043i	1.65387	−	6.17233i	−34.3945	−	10.6310i	−3.60318	+	6.24089i	−63.3317	+	9.22467i	62.1618	+	51.9318i	−5.41791	+	24.9794i
43.2	−3.99271	−	0.241452i	−8.96823	−	0.755499i	15.8834	+	1.92809i	4.46233	−	16.6536i	35.6251	+	5.18188i	−26.5691	+	46.0190i	−62.9522	−	11.5334i	79.8584	+	13.5510i	−21.8378	+	65.4157i
43.3	−3.98762	−	0.314439i	3.15271	−	8.42974i	15.8023	+	2.50773i	7.42807	−	27.7219i	−15.2224	+	32.6233i	34.7350	−	60.1627i	−62.2249	−	14.9687i	−61.1209	−	53.1530i	−38.3372	+	108.209i
43.4	−3.98004	+	0.399129i	0.914310	+	8.95344i	15.6814	−	3.17710i	−6.62631	+	24.7297i	−7.21257	−	35.2701i	29.7045	−	51.4497i	−61.1444	+	18.9039i	−79.3281	+	16.3724i	16.5026	−	101.070i
43.5	−3.97612	+	0.436417i	6.86305	−	5.82225i	15.6191	−	3.47049i	−0.256829	+	0.958498i	−24.7474	+	26.1451i	−20.2926	+	35.1479i	−60.5888	+	20.6155i	13.2028	−	79.9167i	0.602878	−	3.92319i
43.6	−3.92871	+	0.751818i	−6.25625	+	6.46988i	14.8695	−	5.90735i	10.2172	−	38.1310i	19.7148	−	30.1219i	46.2354	−	80.0821i	−53.9769	+	34.3875i	−2.71874	−	80.9544i	−11.4727	+	157.487i
43.7	−3.91809	−	0.805336i	−0.286582	+	8.99544i	14.7029	+	6.31076i	−6.58804	+	24.5869i	8.36721	−	35.0141i	−29.6259	+	51.3136i	−52.5249	−	36.5669i	−80.8357	−	5.15587i	45.6132	−	91.0281i
43.8	−3.85908	+	1.05237i	−8.88580	+	1.42918i	13.7850	−	8.12234i	−8.22858	+	30.7095i	32.7870	−	14.8664i	2.18606	−	3.78637i	−44.6500	+	45.8517i	76.9149	−	25.3988i	−0.562858	−	127.170i
43.9	−3.85405	−	1.07066i	−2.43677	−	8.66384i	13.7074	+	8.25275i	−9.48785	+	35.4091i	0.115413	+	35.9998i	−24.7419	+	42.8542i	−43.9930	−	46.4824i	−69.1243	+	42.2236i	74.4778	−	126.310i
43.10	−3.79505	−	1.26396i	−7.41081	−	5.10685i	12.8048	+	9.59362i	3.73758	−	13.9489i	21.6695	+	28.7477i	12.2022	−	21.1348i	−36.4688	−	52.5930i	28.8402	+	75.6917i	−31.8152	+	48.2124i
43.11	−3.71400	−	1.48532i	8.63489	−	2.53745i	11.5877	+	11.0330i	−12.5232	+	46.7374i	−35.8389	−	3.40148i	34.1494	−	59.1485i	−26.6492	−	58.1878i	68.1227	−	43.8211i	115.931	−	154.982i
43.12	−3.71086	−	1.49316i	0.0704167	+	8.99972i	11.5409	+	11.0818i	12.0256	−	44.8802i	13.1767	−	33.5019i	−27.0835	+	46.9099i	−26.2799	−	58.3555i	−80.9901	+	1.26746i	−111.639	+	148.588i
43.13	−3.69852	+	1.52347i	−4.19539	−	7.96233i	11.3581	−	11.2692i	−5.26331	+	19.6429i	27.6471	+	23.0573i	20.6959	−	35.8464i	−24.8399	+	58.9829i	−45.7974	+	66.8102i	−10.4590	−	80.6683i
43.14	−3.65519	+	1.62467i	−1.84438	−	8.80899i	10.7209	−	11.8770i	9.79442	−	36.5533i	21.0533	+	29.2020i	−44.3913	+	76.8880i	−19.8907	+	60.8306i	−74.1965	+	32.4943i	23.5866	+	149.522i
43.15	−3.46839	+	1.99255i	3.67715	+	8.21453i	8.05949	−	13.8219i	5.27287	−	19.6786i	−29.1217	−	21.1643i	−3.25457	+	5.63709i	−0.412693	+	63.9987i	−53.9572	+	60.4121i	20.9222	+	78.7596i
43.16	−3.44308	−	2.03597i	7.68217	+	4.68873i	7.70964	+	14.0200i	5.93355	−	22.1443i	−16.9042	−	31.7844i	24.2205	−	41.9511i	1.99948	−	63.9688i	37.0316	+	72.0393i	−65.5149	+	64.1642i
43.17	−3.40191	+	2.10405i	−5.52624	+	7.10356i	7.14596	−	14.3156i	0.532947	−	1.98899i	3.85354	−	35.7932i	−35.7553	+	61.9300i	5.81071	+	63.7357i	−19.9213	−	78.5121i	2.37188	+	7.88769i
43.18	−3.39483	−	2.11545i	−6.80020	+	5.89553i	7.04972	+	14.3632i	−2.47493	+	9.23658i	35.5572	−	5.62879i	10.9438	−	18.9553i	6.45210	−	63.6739i	11.4855	−	80.1816i	27.9415	−	26.1210i
43.19	−3.27178	−	2.30119i	2.69878	−	8.58584i	5.40905	+	15.0580i	0.991730	−	3.70119i	−28.5875	+	21.8805i	0.0966262	−	0.167361i	16.9540	−	61.7135i	−66.4331	−	46.3426i	−11.7618	+	9.82730i
43.20	−3.23777	+	2.34879i	6.41750	−	6.30997i	4.96634	−	15.2097i	−4.16032	+	15.5265i	−5.95758	+	35.5036i	24.2180	−	41.9468i	19.6446	+	60.9105i	1.36853	−	80.9884i	−22.9984	−	60.0431i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner
16.f	odd	4	1	inner
144.v	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	144.5.v.a	✓	376
9.c	even	3	1	inner	144.5.v.a	✓	376
16.f	odd	4	1	inner	144.5.v.a	✓	376
144.v	odd	12	1	inner	144.5.v.a	✓	376

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.5.v.a	✓	376	1.a	even	1	1	trivial
144.5.v.a	✓	376	9.c	even	3	1	inner
144.5.v.a	✓	376	16.f	odd	4	1	inner
144.5.v.a	✓	376	144.v	odd	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(144, [\chi])\).