Newform orbit 180.3.v.a

• Label: 180.3.v.a
• Level: $180$
• Weight: $3$
• Character orbit: 180.v
• Analytic conductor: $4.905$
• Analytic rank: $0$
• Dimension: $272$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.90464475849\)
Analytic rank:	\(0\)
Dimension:	\(272\)
Relative dimension:	\(68\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 272 q - 6 q^{2} - 12 q^{5} - 8 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
23.1	−1.99882	+	0.0686169i	−0.866619	−	2.87210i	3.99058	−	0.274306i	−1.69193	−	4.70504i	1.92929	+	5.68136i	2.60652	−	9.72768i	−7.95765	+	0.822110i	−7.49794	+	4.97804i	3.70472	+	9.28844i
23.2	−1.99843	+	0.0792022i	2.33394	+	1.88487i	3.98745	−	0.316560i	3.77346	+	3.28040i	−4.81350	−	3.58193i	−3.10586	+	11.5912i	−7.94358	+	0.948438i	1.89452	+	8.79834i	−7.80081	−	6.25679i
23.3	−1.98234	−	0.265231i	1.57971	−	2.55040i	3.85930	+	1.05155i	−4.16508	+	2.76625i	−3.80795	+	4.63676i	−0.704888	+	2.63068i	−7.37153	−	3.10814i	−4.00906	−	8.05776i	8.99027	−	4.37893i
23.4	−1.97810	−	0.295138i	−2.70010	+	1.30745i	3.82579	+	1.16763i	−2.81240	−	4.13406i	5.72696	−	1.78938i	−1.42055	+	5.30156i	−7.22319	−	3.43882i	5.58113	−	7.06053i	4.34310	+	9.00764i
23.5	−1.96254	+	0.385279i	−2.90870	+	0.734496i	3.70312	−	1.51225i	0.178560	+	4.99681i	5.42544	−	2.56214i	0.293647	−	1.09590i	−6.68488	+	4.39458i	7.92103	−	4.27285i	−2.27560	−	9.73764i
23.6	−1.94032	−	0.484928i	−0.800208	+	2.89131i	3.52969	+	1.88183i	4.85522	−	1.19451i	2.95474	−	5.22202i	2.17593	−	8.12068i	−5.93618	−	5.36301i	−7.71933	−	4.62730i	−9.99993	−	0.0367095i
23.7	−1.88318	+	0.673514i	2.99492	+	0.174594i	3.09276	−	2.53670i	−4.59989	−	1.95984i	−5.75757	+	1.68832i	−1.17779	+	4.39555i	−4.11573	+	6.86008i	8.93903	+	1.04579i	9.98242	+	0.592652i
23.8	−1.88005	−	0.682202i	−1.02400	−	2.81983i	3.06920	+	2.56515i	4.94759	+	0.722068i	0.00147966	+	6.00000i	−2.05019	+	7.65143i	−4.02031	−	6.91644i	−6.90286	+	5.77500i	−8.80913	−	4.73278i
23.9	−1.84909	+	0.762148i	0.204521	+	2.99302i	2.83826	−	2.81856i	−4.76159	+	1.52554i	−2.65930	−	5.37849i	2.15711	−	8.05045i	−3.10004	+	7.37494i	−8.91634	+	1.22427i	7.64192	−	6.44989i
23.10	−1.83285	+	0.800411i	2.64894	−	1.40823i	2.71869	−	2.93407i	4.99999	+	0.00771995i	−3.72794	+	4.70132i	2.27318	−	8.48361i	−2.63449	+	7.55377i	5.03375	−	7.46065i	−9.17042	+	3.98790i
23.11	−1.76475	−	0.941089i	2.81520	+	1.03666i	2.22870	+	3.32158i	−1.08683	+	4.88045i	−3.99253	−	4.47881i	2.90708	−	10.8494i	−0.807202	−	7.95917i	6.85065	+	5.83683i	6.51093	−	7.58998i
23.12	−1.74814	+	0.971592i	−2.72685	−	1.25071i	2.11202	−	3.39697i	4.18642	−	2.73385i	5.98211	−	0.462971i	−1.08898	+	4.06412i	−0.391643	+	7.99041i	5.87146	+	6.82100i	−4.66227	+	8.84665i
23.13	−1.69861	−	1.05581i	2.75442	−	1.18876i	1.77052	+	3.58682i	1.89315	−	4.62774i	−5.93379	−	0.888911i	−0.668907	+	2.49640i	0.779590	−	7.96192i	6.17368	−	6.54872i	−8.10174	+	5.86189i
23.14	−1.61680	+	1.17726i	−0.319431	+	2.98295i	1.22810	−	3.80680i	2.64586	−	4.24257i	−2.99525	−	5.19889i	−1.90052	+	7.09282i	2.49601	+	7.60065i	−8.79593	−	1.90569i	0.716781	+	9.97428i
23.15	−1.60157	−	1.19790i	−2.57707	−	1.53581i	1.13006	+	3.83705i	−3.99036	+	3.01281i	2.28762	+	5.54678i	−0.0614024	+	0.229157i	2.78654	−	7.49901i	4.28260	+	7.91576i	9.99990	−	0.0451586i
23.16	−1.60019	+	1.19975i	−0.110713	−	2.99796i	1.12121	−	3.83965i	0.524705	+	4.97239i	3.77396	+	4.66447i	−0.633651	+	2.36482i	2.81247	+	7.48933i	−8.97549	+	0.663825i	−6.80525	−	7.32725i
23.17	−1.58088	−	1.22509i	1.16828	+	2.76317i	0.998333	+	3.87341i	−4.13729	−	2.80764i	1.53822	−	5.79947i	−0.967290	+	3.60997i	3.16702	−	7.34643i	−6.27025	+	6.45631i	3.10094	+	9.50706i
23.18	−1.30527	−	1.51535i	−1.56620	+	2.55871i	−0.592542	+	3.95587i	1.35415	+	4.81313i	5.92165	−	0.966477i	−0.979164	+	3.65429i	6.76793	−	4.26557i	−4.09403	−	8.01492i	5.52602	−	8.33445i
23.19	−1.20757	+	1.59429i	−2.67197	−	1.36403i	−1.08354	−	3.85045i	−4.99807	+	0.138956i	5.40126	−	2.61274i	1.71830	−	6.41279i	7.44719	+	2.92221i	5.27885	+	7.28929i	5.81399	−	8.13619i
23.20	−1.13981	−	1.64342i	−2.97923	−	0.352382i	−1.40165	+	3.74638i	2.14586	−	4.51611i	2.81666	+	5.29778i	3.02532	−	11.2907i	7.75450	−	1.96667i	8.75165	+	2.09965i	−9.86775	+	1.62098i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.c	odd	4	1	inner
9.d	odd	6	1	inner
20.e	even	4	1	inner
36.h	even	6	1	inner
45.l	even	12	1	inner
180.v	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	180.3.v.a	✓	272
4.b	odd	2	1	inner	180.3.v.a	✓	272
5.c	odd	4	1	inner	180.3.v.a	✓	272
9.d	odd	6	1	inner	180.3.v.a	✓	272
20.e	even	4	1	inner	180.3.v.a	✓	272
36.h	even	6	1	inner	180.3.v.a	✓	272
45.l	even	12	1	inner	180.3.v.a	✓	272
180.v	odd	12	1	inner	180.3.v.a	✓	272

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
180.3.v.a	✓	272	1.a	even	1	1	trivial
180.3.v.a	✓	272	4.b	odd	2	1	inner
180.3.v.a	✓	272	5.c	odd	4	1	inner
180.3.v.a	✓	272	9.d	odd	6	1	inner
180.3.v.a	✓	272	20.e	even	4	1	inner
180.3.v.a	✓	272	36.h	even	6	1	inner
180.3.v.a	✓	272	45.l	even	12	1	inner
180.3.v.a	✓	272	180.v	odd	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(180, [\chi])\).