Newform orbit 287.3.v.a

• Label: 287.3.v.a
• Level: $287$
• Weight: $3$
• Character orbit: 287.v
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $432$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.v (of order \(24\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(432\)
Relative dimension:	\(54\) over \(\Q(\zeta_{24})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 432 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 48 q^{8} - 36 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
44.1	−1.00113	−	3.73626i	4.33433	−	0.570626i	−9.49326	+	5.48094i	6.12199	−	1.64038i	−6.47122	−	15.6229i	−6.59685	−	2.34128i	19.0416	+	19.0416i	9.76749	−	2.61719i	−12.2578	−	21.2311i
44.2	−0.964481	−	3.59949i	−2.15102	+	0.283187i	−8.56202	+	4.94329i	4.97373	−	1.33271i	3.09394	+	7.46944i	6.47657	+	2.65595i	15.5112	+	15.5112i	−4.14666	+	1.11109i	−9.59414	−	16.6175i
44.3	−0.953963	−	3.56024i	3.93802	−	0.518450i	−8.30116	+	4.79268i	−6.13448	+	1.64373i	−5.60253	−	13.5257i	2.91136	+	6.36584i	14.5570	+	14.5570i	6.54587	−	1.75396i	11.7041	+	20.2722i
44.4	−0.934785	−	3.48866i	0.164201	−	0.0216175i	−7.83285	+	4.52230i	−1.38302	+	0.370580i	−0.228909	−	0.552635i	0.440489	−	6.98613i	12.8833	+	12.8833i	−8.66684	+	2.32227i	2.58566	+	4.47849i
44.5	−0.895161	−	3.34079i	−2.33888	+	0.307920i	−6.89545	+	3.98109i	−6.16719	+	1.65249i	3.12237	+	7.53807i	−5.68361	+	4.08615i	9.69000	+	9.69000i	−3.31778	+	0.888995i	11.0413	+	19.1240i
44.6	−0.845521	−	3.15553i	−5.30986	+	0.699057i	−5.77835	+	3.33613i	−4.43760	+	1.18905i	6.69550	+	16.1644i	6.89536	+	1.20580i	6.17295	+	6.17295i	19.0126	−	5.09442i	7.50417	+	12.9976i
44.7	−0.822999	−	3.07147i	−0.665898	+	0.0876672i	−5.29251	+	3.05563i	6.18603	−	1.65754i	0.817301	+	1.97314i	−2.80548	+	6.41321i	4.74713	+	4.74713i	−8.25760	+	2.21262i	−10.1822	−	17.6361i
44.8	−0.805923	−	3.00775i	2.67346	−	0.351967i	−4.93293	+	2.84803i	−4.41031	+	1.18174i	−3.21323	−	7.75742i	6.30583	−	3.03916i	3.73441	+	3.73441i	−1.66984	+	0.447433i	7.10875	+	12.3127i
44.9	−0.743556	−	2.77499i	−4.02310	+	0.529651i	−3.68360	+	2.12672i	5.12912	−	1.37434i	4.46118	+	10.7702i	−1.22522	−	6.89194i	0.514865	+	0.514865i	7.21145	−	1.93230i	−7.62758	−	13.2113i
44.10	−0.711148	−	2.65404i	4.57597	−	0.602438i	−3.07410	+	1.77483i	5.06808	−	1.35799i	−4.85309	−	11.7164i	5.42371	+	4.42530i	−0.874947	−	0.874947i	11.8832	−	3.18410i	−7.20831	−	12.4852i
44.11	−0.669740	−	2.49950i	1.94687	−	0.256310i	−2.33487	+	1.34804i	−2.15743	+	0.578081i	−1.94454	−	4.69454i	−6.88381	−	1.27009i	−2.38587	−	2.38587i	−4.96873	+	1.33137i	2.88983	+	5.00534i
44.12	−0.605293	−	2.25898i	5.84002	−	0.768853i	−1.27252	+	0.734692i	−4.08855	+	1.09552i	−5.27175	−	12.7271i	−1.90551	−	6.73565i	−4.18485	−	4.18485i	24.8213	−	6.65085i	4.94953	+	8.57284i
44.13	−0.601567	−	2.24508i	−4.60009	+	0.605614i	−1.21439	+	0.701128i	1.97238	−	0.528497i	4.12691	+	9.96325i	−6.51687	+	2.55546i	−4.26942	−	4.26942i	12.1007	−	3.24239i	−2.37303	−	4.11021i
44.14	−0.585405	−	2.18476i	2.68487	−	0.353470i	−0.966375	+	0.557937i	7.59297	−	2.03453i	−2.34399	−	5.65888i	2.78312	−	6.42295i	−4.61274	−	4.61274i	−1.60972	+	0.431323i	−8.88992	−	15.3978i
44.15	−0.518206	−	1.93397i	−0.899559	+	0.118429i	−0.00760404	+	0.00439020i	−3.55516	+	0.952603i	0.695196	+	1.67835i	5.90938	+	3.75223i	−5.65063	−	5.65063i	−7.89815	+	2.11630i	3.68461	+	6.38194i
44.16	−0.472662	−	1.76400i	−3.59669	+	0.473513i	0.575817	−	0.332448i	−8.51355	+	2.28120i	2.53530	+	6.12074i	−2.12311	−	6.67026i	−6.02395	−	6.02395i	4.01862	−	1.07679i	8.04807	+	13.9397i
44.17	−0.472042	−	1.76168i	0.937698	−	0.123450i	0.583396	−	0.336824i	2.21585	−	0.593735i	−0.660113	−	1.59365i	2.05508	+	6.69153i	−6.02733	−	6.02733i	−7.82930	+	2.09785i	−2.09195	−	3.62336i
44.18	−0.432281	−	1.61329i	−1.08853	+	0.143308i	1.04825	−	0.605209i	−2.34666	+	0.628787i	0.701750	+	1.69417i	5.57803	−	4.22914i	−6.15357	−	6.15357i	−7.52897	+	2.01738i	2.02884	+	3.51405i
44.19	−0.358555	−	1.33815i	2.81232	−	0.370250i	1.80203	−	1.04040i	−9.33412	+	2.50107i	−1.50382	−	3.63054i	−3.19103	+	6.23036i	−5.95670	−	5.95670i	−0.921246	+	0.246847i	6.69359	+	11.5936i
44.20	−0.345775	−	1.29045i	0.635300	−	0.0836388i	1.91841	−	1.10759i	7.27076	−	1.94819i	−0.327602	−	0.790901i	−5.53537	−	4.28481i	−5.87132	−	5.87132i	−8.29672	+	2.22310i	−5.02809	−	8.70890i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner
41.e	odd	8	1	inner
287.v	odd	24	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	287.3.v.a	✓	432
7.c	even	3	1	inner	287.3.v.a	✓	432
41.e	odd	8	1	inner	287.3.v.a	✓	432
287.v	odd	24	1	inner	287.3.v.a	✓	432

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
287.3.v.a	✓	432	1.a	even	1	1	trivial
287.3.v.a	✓	432	7.c	even	3	1	inner
287.3.v.a	✓	432	41.e	odd	8	1	inner
287.3.v.a	✓	432	287.v	odd	24	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(287, [\chi])\).