Newform orbit 287.3.y.a

• Label: 287.3.y.a
• Level: $287$
• Weight: $3$
• Character orbit: 287.y
• 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.y (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(432\)
Relative dimension:	\(54\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 432 q - 3 q^{2} - 24 q^{3} + 101 q^{4} - 9 q^{5} - 6 q^{7} - 16 q^{8} + 576 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
10.1	−0.407277	+	3.87498i	−4.43919	−	2.56297i	−10.9370	−	2.32473i	−1.15474	−	1.03974i	11.7394	−	16.1579i	−5.75629	−	3.98310i	8.64655	−	26.6114i	8.63759	+	14.9607i	4.49926	−	4.05115i
10.2	−0.395467	+	3.76261i	1.42023	+	0.819968i	−10.0883	−	2.14433i	−2.55057	−	2.29654i	−3.64688	+	5.01950i	−2.63679	−	6.48439i	7.38140	−	22.7176i	−3.15530	−	5.46515i	9.64968	−	8.68861i
10.3	−0.377653	+	3.59313i	1.08377	+	0.625718i	−8.85534	−	1.88226i	−2.01323	−	1.81272i	−2.65757	+	3.65783i	−0.128124	+	6.99883i	5.64163	−	17.3631i	−3.71695	−	6.43795i	7.27365	−	6.54922i
10.4	−0.372260	+	3.54182i	2.27091	+	1.31111i	−8.49333	−	1.80531i	5.49683	+	4.94937i	−5.48909	+	7.55509i	6.95621	−	0.781768i	5.15378	−	15.8617i	−1.06198	−	1.83940i	−19.5760	+	17.6264i
10.5	−0.352334	+	3.35223i	4.51935	+	2.60925i	−7.20072	−	1.53056i	2.89418	+	2.60593i	−10.3391	+	14.2306i	−6.73483	+	1.90841i	3.50144	−	10.7763i	9.11637	+	15.7900i	−9.75540	+	8.78380i
10.6	−0.350757	+	3.33723i	−2.35294	−	1.35847i	−7.10146	−	1.50946i	−4.71627	−	4.24655i	5.35883	−	7.37579i	6.89642	+	1.19976i	3.38054	−	10.4042i	−0.809124	−	1.40144i	15.8260	−	14.2498i
10.7	−0.342604	+	3.25966i	−2.07689	−	1.19909i	−6.59542	−	1.40190i	4.83955	+	4.35755i	4.62020	−	6.35915i	3.55259	−	6.03151i	2.77798	−	8.54975i	−1.62434	−	2.81344i	−15.8622	+	14.2824i
10.8	−0.340799	+	3.24249i	−3.64025	−	2.10170i	−6.48498	−	1.37843i	4.03434	+	3.63253i	8.05533	−	11.0872i	2.25115	+	6.62815i	2.64959	−	8.15460i	4.33429	+	7.50720i	−13.1533	+	11.8433i
10.9	−0.288646	+	2.74628i	−0.0116820	−	0.00674463i	−3.54617	−	0.753762i	4.04208	+	3.63950i	0.0218947	−	0.0301354i	−6.18024	−	3.28704i	−0.319659	+	0.983810i	−4.49991	−	7.79407i	−11.1618	+	10.0502i
10.10	−0.282410	+	2.68695i	−1.99951	−	1.15441i	−3.22738	−	0.686000i	0.0649077	+	0.0584432i	3.66654	−	5.04656i	−6.98405	+	0.472222i	−0.584859	+	1.80001i	−1.83465	−	3.17771i	−0.175365	+	0.157899i
10.11	−0.276618	+	2.63184i	1.67521	+	0.967181i	−2.93749	−	0.624382i	−5.03132	−	4.53022i	−3.00886	+	4.14134i	0.936757	−	6.93704i	−0.815219	+	2.50899i	−2.62912	−	4.55377i	13.3146	−	11.9885i
10.12	−0.262361	+	2.49620i	3.99634	+	2.30729i	−2.24959	−	0.478164i	−1.09445	−	0.985445i	−6.80793	+	9.37031i	6.92637	+	1.01262i	−1.31867	+	4.05845i	6.14714	+	10.6472i	2.74701	−	2.47342i
10.13	−0.256802	+	2.44330i	3.72271	+	2.14931i	−1.99119	−	0.423241i	−6.18690	−	5.57071i	−6.20740	+	8.54375i	−6.03910	+	3.53967i	−1.49128	+	4.58968i	4.73903	+	8.20823i	15.1997	−	13.6859i
10.14	−0.223775	+	2.12907i	−4.20842	−	2.42973i	−0.570287	−	0.121218i	−4.07393	−	3.66818i	6.11481	−	8.41631i	0.752068	−	6.95948i	−2.26048	+	6.95703i	7.30717	+	12.6564i	8.72148	−	7.85285i
10.15	−0.197672	+	1.88072i	−2.25015	−	1.29912i	0.414549	+	0.0881151i	−2.05729	−	1.85239i	2.88808	−	3.97510i	6.85731	−	1.40618i	−2.58517	+	7.95634i	−1.12456	−	1.94779i	3.89051	−	3.50303i
10.16	−0.193036	+	1.83662i	1.95836	+	1.13066i	0.576688	+	0.122579i	6.02254	+	5.42272i	−2.45462	+	3.37850i	−0.339639	+	6.99176i	−2.61914	+	8.06089i	−1.94322	−	3.36575i	−11.1220	+	10.0143i
10.17	−0.182448	+	1.73588i	−4.79904	−	2.77073i	0.932598	+	0.198230i	−1.81832	−	1.63723i	5.68522	−	7.82504i	−1.44156	+	6.84996i	−2.67174	+	8.22277i	10.8538	+	18.7994i	3.17378	−	2.85768i
10.18	−0.181634	+	1.72813i	−0.294892	−	0.170256i	0.959146	+	0.203873i	−1.02853	−	0.926089i	0.347787	−	0.478687i	−1.59260	+	6.81642i	−2.67439	+	8.23091i	−4.44203	−	7.69381i	1.78722	−	1.60922i
10.19	−0.153412	+	1.45962i	0.632396	+	0.365114i	1.80565	+	0.383802i	2.72179	+	2.45071i	−0.629943	+	0.867043i	4.21354	−	5.58982i	−2.65133	+	8.15997i	−4.23338	−	7.33244i	−3.99465	+	3.59680i
10.20	−0.130578	+	1.24237i	4.05852	+	2.34319i	2.38617	+	0.507196i	3.04278	+	2.73974i	−3.44105	+	4.73619i	−2.06147	−	6.68957i	−2.48581	+	7.65054i	6.48104	+	11.2255i	−3.80107	+	3.42250i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
41.d	even	5	1	inner
287.y	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	287.3.y.a	✓	432
7.d	odd	6	1	inner	287.3.y.a	✓	432
41.d	even	5	1	inner	287.3.y.a	✓	432
287.y	odd	30	1	inner	287.3.y.a	✓	432

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
287.3.y.a	✓	432	1.a	even	1	1	trivial
287.3.y.a	✓	432	7.d	odd	6	1	inner
287.3.y.a	✓	432	41.d	even	5	1	inner
287.3.y.a	✓	432	287.y	odd	30	1	inner

Hecke kernels

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