Newform orbit 87.6.i.a

• Label: 87.6.i.a
• Level: $87$
• Weight: $6$
• Character orbit: 87.i
• Analytic conductor: $13.953$
• Analytic rank: $0$
• Dimension: $144$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	87.i (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.9533923237\)
Analytic rank:	\(0\)
Dimension:	\(144\)
Relative dimension:	\(24\) over \(\Q(\zeta_{14})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 144 q + 396 q^{4} + 196 q^{5} - 72 q^{6} + 120 q^{7} + 1944 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−10.2651	−	2.34294i	3.90495	+	8.10872i	71.0518	+	34.2168i	23.6845	−	103.768i	−21.0865	−	92.3859i	64.1176	−	30.8774i	−385.763	−	307.636i	−50.5027	+	63.3284i	−486.247	+	1009.70i
4.2	−9.53750	−	2.17687i	3.90495	+	8.10872i	57.3941	+	27.6395i	−7.42093	+	32.5132i	−19.5918	−	85.8375i	−217.219	+	104.607i	−242.477	−	193.369i	−50.5027	+	63.3284i	141.554	−	293.940i
4.3	−9.20078	−	2.10002i	−3.90495	−	8.10872i	51.4132	+	24.7593i	5.79994	−	25.4112i	18.9002	+	82.8070i	−66.3263	+	31.9410i	−184.936	−	147.481i	−50.5027	+	63.3284i	−106.728	+	221.623i
4.4	−9.03870	−	2.06302i	−3.90495	−	8.10872i	48.6111	+	23.4098i	7.88431	−	34.5434i	18.5672	+	81.3483i	119.505	−	57.5508i	−159.134	−	126.905i	−50.5027	+	63.3284i	−142.528	+	295.962i
4.5	−8.27191	−	1.88801i	−3.90495	−	8.10872i	36.0289	+	17.3506i	−22.4972	+	98.5667i	16.9921	+	74.4472i	−55.8518	+	26.8968i	−52.9961	−	42.2630i	−50.5027	+	63.3284i	372.190	−	772.860i
4.6	−8.17438	−	1.86575i	3.90495	+	8.10872i	34.5084	+	16.6184i	−10.8036	+	47.3335i	−16.7917	−	73.5694i	147.932	−	71.2405i	−41.3082	−	32.9422i	−50.5027	+	63.3284i	176.625	−	366.765i
4.7	−4.84278	−	1.10533i	3.90495	+	8.10872i	−6.60023	−	3.17851i	14.4210	−	63.1827i	−9.94800	−	43.5850i	94.2226	−	45.3752i	152.726	+	121.795i	−50.5027	+	63.3284i	−139.676	+	290.040i
4.8	−3.99650	−	0.912174i	−3.90495	−	8.10872i	−13.6911	−	6.59328i	12.6469	−	55.4098i	8.20957	+	35.9685i	201.066	−	96.8280i	151.260	+	120.626i	−50.5027	+	63.3284i	−101.087	+	209.909i
4.9	−3.74950	−	0.855799i	−3.90495	−	8.10872i	−15.5046	−	7.46664i	−2.59268	+	11.3593i	7.70219	+	33.7455i	−116.542	+	56.1239i	147.964	+	117.998i	−50.5027	+	63.3284i	19.4425	−	40.3729i
4.10	−3.19616	−	0.729503i	3.90495	+	8.10872i	−19.1477	−	9.22106i	−19.1896	+	84.0752i	−6.56553	−	28.7655i	−67.0118	+	32.2712i	136.492	+	108.849i	−50.5027	+	63.3284i	122.666	−	254.719i
4.11	−2.20321	−	0.502869i	3.90495	+	8.10872i	−24.2297	−	11.6684i	10.6270	−	46.5600i	−4.52582	−	19.8289i	−118.835	+	57.2280i	104.054	+	82.9807i	−50.5027	+	63.3284i	−46.8271	+	97.2375i
4.12	1.14784	+	0.261988i	3.90495	+	8.10872i	−27.5821	−	13.2828i	−5.77295	+	25.2930i	2.35789	+	10.3306i	201.777	−	97.1706i	−57.6360	−	45.9632i	−50.5027	+	63.3284i	−13.2529	+	27.5199i
4.13	1.27890	+	0.291900i	−3.90495	−	8.10872i	−27.2806	−	13.1377i	23.1449	−	101.404i	−2.62710	−	11.5101i	−75.7179	+	36.4638i	−63.8733	−	50.9372i	−50.5027	+	63.3284i	59.1999	−	122.930i
4.14	1.29897	+	0.296482i	−3.90495	−	8.10872i	−27.2316	−	13.1140i	−0.650303	+	2.84916i	−2.66834	−	11.6907i	6.19422	−	2.98298i	−64.8192	−	51.6916i	−50.5027	+	63.3284i	−1.68945	+	3.50818i
4.15	2.38556	+	0.544490i	−3.90495	−	8.10872i	−23.4366	−	11.2865i	−20.8554	+	91.3735i	−4.90041	−	21.4701i	114.478	−	55.1298i	−110.982	−	88.5055i	−50.5027	+	63.3284i	−99.5039	+	206.622i
4.16	2.86445	+	0.653793i	3.90495	+	8.10872i	−21.0534	−	10.1388i	3.27765	−	14.3603i	5.88414	+	25.7801i	70.8911	−	34.1394i	−127.185	−	101.427i	−50.5027	+	63.3284i	18.7773	−	38.9915i
4.17	5.13309	+	1.17159i	3.90495	+	8.10872i	−3.85504	−	1.85649i	15.5469	−	68.1156i	10.5443	+	46.1978i	−203.060	+	97.7886i	−149.339	−	119.094i	−50.5027	+	63.3284i	159.608	−	331.429i
4.18	5.48588	+	1.25212i	3.90495	+	8.10872i	−0.303898	−	0.146350i	−14.3721	+	62.9684i	11.2691	+	49.3729i	−36.8119	+	17.7277i	−142.263	−	113.451i	−50.5027	+	63.3284i	−157.687	+	327.441i
4.19	5.95516	+	1.35923i	−3.90495	−	8.10872i	4.78541	+	2.30453i	4.98722	−	21.8504i	−12.2330	−	53.5964i	79.4228	−	38.2480i	−127.456	−	101.643i	−50.5027	+	63.3284i	59.3994	−	123.344i
4.20	7.54091	+	1.72116i	−3.90495	−	8.10872i	25.0719	+	12.0740i	−14.3003	+	62.6535i	−15.4905	−	67.8682i	−156.112	+	75.1797i	−25.2315	−	20.1215i	−50.5027	+	63.3284i	−215.674	+	447.851i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
29.e	even	14	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	87.6.i.a	✓	144
29.e	even	14	1	inner	87.6.i.a	✓	144

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
87.6.i.a	✓	144	1.a	even	1	1	trivial
87.6.i.a	✓	144	29.e	even	14	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(87, [\chi])\).