Newform orbit 87.4.f.a

• Label: 87.4.f.a
• Level: $87$
• Weight: $4$
• Character orbit: 87.f
• Analytic conductor: $5.133$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	87.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.13316617050\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(28\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 2 q^{3} - 8 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1	−3.93815	−	3.93815i	4.17442	−	3.09422i			23.0180i	4.20248			−28.6250	−	4.25398i	23.9842			59.1430	−	59.1430i	7.85158	−	25.8332i	−16.5500	−	16.5500i
17.2	−3.58770	−	3.58770i	1.94238	+	4.81946i			17.7432i	9.58509			10.3221	−	24.2595i	−28.9392			34.9558	−	34.9558i	−19.4543	+	18.7224i	−34.3885	−	34.3885i
17.3	−3.49423	−	3.49423i	−4.04261	+	3.26455i			16.4193i	−21.4900			25.5329	+	2.71875i	−6.50988			29.4191	−	29.4191i	5.68547	−	26.3946i	75.0911	+	75.0911i
17.4	−3.10556	−	3.10556i	−5.19199	+	0.208054i			11.2890i	12.2499			16.7702	+	15.4779i	15.2934			10.2143	−	10.2143i	26.9134	−	2.16042i	−38.0430	−	38.0430i
17.5	−2.99703	−	2.99703i	−1.94175	−	4.81971i			9.96439i	−1.78460			−8.62533	+	20.2643i	−13.0681			5.88734	−	5.88734i	−19.4592	+	18.7174i	5.34851	+	5.34851i
17.6	−2.65475	−	2.65475i	3.46189	+	3.87496i			6.09543i	−10.6209			1.09662	−	19.4775i	21.3715			−5.05617	+	5.05617i	−3.03069	+	26.8294i	28.1959	+	28.1959i
17.7	−2.33225	−	2.33225i	4.54230	−	2.52338i			2.87876i	−9.43014			−16.4789	−	4.70862i	−10.3502			−11.9440	+	11.9440i	14.2651	−	22.9240i	21.9934	+	21.9934i
17.8	−1.93052	−	1.93052i	5.00186	+	1.40760i		−	0.546205i	15.4049			−6.93878	−	12.3736i	−1.06428			−16.4986	+	16.4986i	23.0373	+	14.0813i	−29.7394	−	29.7394i
17.9	−1.67669	−	1.67669i	−3.07207	+	4.19075i		−	2.37743i	9.43188			12.1775	−	1.87566i	−17.8269			−17.3997	+	17.3997i	−8.12472	−	25.7486i	−15.8143	−	15.8143i
17.10	−1.14976	−	1.14976i	−1.44273	+	4.99185i		−	5.35608i	−3.21080			7.39824	−	4.08065i	13.8985			−15.3563	+	15.3563i	−22.8371	−	14.4038i	3.69167	+	3.69167i
17.11	−1.13876	−	1.13876i	0.521672	−	5.16990i		−	5.40645i	15.0739			−6.48134	+	5.29322i	34.6060			−15.2667	+	15.2667i	−26.4557	−	5.39398i	−17.1656	−	17.1656i
17.12	−1.00610	−	1.00610i	−4.82292	−	1.93376i		−	5.97553i	−12.1103			2.90678	+	6.79789i	10.9956			−14.0608	+	14.0608i	19.5211	+	18.6528i	12.1841	+	12.1841i
17.13	−0.355235	−	0.355235i	1.34585	−	5.01883i		−	7.74762i	−7.35852			−2.26096	+	1.30477i	−9.57542			−5.59410	+	5.59410i	−23.3774	−	13.5092i	2.61400	+	2.61400i
17.14	−0.0238580	−	0.0238580i	−4.25761	−	2.97872i		−	7.99886i	17.5231			0.0305118	+	0.172644i	−34.8153			−0.381701	+	0.381701i	9.25449	+	25.3644i	−0.418066	−	0.418066i
17.15	0.0238580	+	0.0238580i	2.97872	+	4.25761i		−	7.99886i	−17.5231			−0.0305118	+	0.172644i	−34.8153			0.381701	−	0.381701i	−9.25449	+	25.3644i	−0.418066	−	0.418066i
17.16	0.355235	+	0.355235i	5.01883	−	1.34585i		−	7.74762i	7.35852			2.26096	+	1.30477i	−9.57542			5.59410	−	5.59410i	23.3774	−	13.5092i	2.61400	+	2.61400i
17.17	1.00610	+	1.00610i	1.93376	+	4.82292i		−	5.97553i	12.1103			−2.90678	+	6.79789i	10.9956			14.0608	−	14.0608i	−19.5211	+	18.6528i	12.1841	+	12.1841i
17.18	1.13876	+	1.13876i	5.16990	−	0.521672i		−	5.40645i	−15.0739			6.48134	+	5.29322i	34.6060			15.2667	−	15.2667i	26.4557	−	5.39398i	−17.1656	−	17.1656i
17.19	1.14976	+	1.14976i	−4.99185	+	1.44273i		−	5.35608i	3.21080			−7.39824	−	4.08065i	13.8985			15.3563	−	15.3563i	22.8371	−	14.4038i	3.69167	+	3.69167i
17.20	1.67669	+	1.67669i	−4.19075	+	3.07207i		−	2.37743i	−9.43188			−12.1775	−	1.87566i	−17.8269			17.3997	−	17.3997i	8.12472	−	25.7486i	−15.8143	−	15.8143i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
29.c	odd	4	1	inner
87.f	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	87.4.f.a	✓	56
3.b	odd	2	1	inner	87.4.f.a	✓	56
29.c	odd	4	1	inner	87.4.f.a	✓	56
87.f	even	4	1	inner	87.4.f.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
87.4.f.a	✓	56	1.a	even	1	1	trivial
87.4.f.a	✓	56	3.b	odd	2	1	inner
87.4.f.a	✓	56	29.c	odd	4	1	inner
87.4.f.a	✓	56	87.f	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(87, [\chi])\).