Newform orbit 55.4.g.b

• Label: 55.4.g.b
• Level: $55$
• Weight: $4$
• Character orbit: 55.g
• Analytic conductor: $3.245$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	55.g (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.24510505032\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 6 q^{2} + 4 q^{3} - 36 q^{4} - 30 q^{5} + 30 q^{6} + 81 q^{7} - 10 q^{8} - 48 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
16.1	−1.43124	−	4.40490i	6.70801	+	4.87365i	−10.8826	+	7.90666i	1.54508	−	4.75528i	11.8672	−	36.5235i	24.3122	−	17.6639i	20.4274	+	14.8414i	12.9014	+	39.7065i	−23.1579
16.2	−1.41210	−	4.34600i	−5.83785	−	4.24145i	−10.4216	+	7.57173i	1.54508	−	4.75528i	−10.1897	+	31.3607i	6.50661	−	4.72733i	18.0477	+	13.1124i	7.74716	+	23.8433i	−22.8483
16.3	−0.513572	−	1.58061i	−1.60233	−	1.16416i	4.23755	−	3.07876i	1.54508	−	4.75528i	−1.01717	+	3.13054i	−7.13418	+	5.18329i	−17.7990	−	12.9317i	−7.13127	−	21.9478i	−8.30978
16.4	0.267133	+	0.822150i	4.45886	+	3.23955i	5.86756	−	4.26304i	1.54508	−	4.75528i	−1.47229	+	4.53124i	−2.26519	+	1.64576i	10.6672	+	7.75016i	1.04327	+	3.21086i	4.32230
16.5	0.849844	+	2.61555i	−5.86409	−	4.26051i	0.353259	−	0.256657i	1.54508	−	4.75528i	6.16003	−	18.9586i	24.9835	−	18.1516i	18.7709	+	13.6378i	7.89215	+	24.2895i	13.7508
16.6	1.50387	+	4.62843i	4.25544	+	3.09176i	−12.6886	+	9.21884i	1.54508	−	4.75528i	−7.91037	+	24.3456i	4.59294	−	3.33697i	−30.2534	−	21.9804i	0.206327	+	0.635008i	24.3331
26.1	−2.96806	−	2.15642i	−0.538187	+	1.65637i	1.68708	+	5.19231i	−4.04508	+	2.93893i	5.16920	−	3.75564i	2.95786	+	9.10335i	−2.88014	+	8.86415i	19.3895	+	14.0873i	18.3436
26.2	−1.81555	−	1.31908i	1.43526	−	4.41727i	−0.915867	−	2.81875i	−4.04508	+	2.93893i	−8.43250	+	6.12657i	−4.84499	−	14.9113i	−7.60317	+	23.4002i	4.39116	+	3.19036i	11.2207
26.3	−0.542122	−	0.393874i	−3.01008	+	9.26408i	−2.33338	−	7.18140i	−4.04508	+	2.93893i	5.28071	−	3.83666i	−6.58487	−	20.2662i	−3.22017	+	9.91067i	−54.9190	−	39.9010i	3.35050
26.4	1.81396	+	1.31792i	2.45444	−	7.55399i	−0.918588	−	2.82712i	−4.04508	+	2.93893i	14.4078	−	10.4679i	−0.510862	−	1.57227i	7.60263	−	23.3985i	−29.1951	−	21.2115i	−11.2109
26.5	2.85482	+	2.07415i	−1.54064	+	4.74160i	1.37577	+	4.23419i	−4.04508	+	2.93893i	−14.2330	+	10.3409i	6.81120	+	20.9627i	3.86880	−	11.9069i	1.73428	+	1.26003i	−17.6438
26.6	4.39302	+	3.19171i	1.08117	−	3.32751i	6.63942	+	20.4340i	−4.04508	+	2.93893i	15.3701	−	11.1670i	−8.32426	−	25.6195i	−22.6286	+	69.6437i	11.9401	+	8.67497i	−27.1503
31.1	−1.43124	+	4.40490i	6.70801	−	4.87365i	−10.8826	−	7.90666i	1.54508	+	4.75528i	11.8672	+	36.5235i	24.3122	+	17.6639i	20.4274	−	14.8414i	12.9014	−	39.7065i	−23.1579
31.2	−1.41210	+	4.34600i	−5.83785	+	4.24145i	−10.4216	−	7.57173i	1.54508	+	4.75528i	−10.1897	−	31.3607i	6.50661	+	4.72733i	18.0477	−	13.1124i	7.74716	−	23.8433i	−22.8483
31.3	−0.513572	+	1.58061i	−1.60233	+	1.16416i	4.23755	+	3.07876i	1.54508	+	4.75528i	−1.01717	−	3.13054i	−7.13418	−	5.18329i	−17.7990	+	12.9317i	−7.13127	+	21.9478i	−8.30978
31.4	0.267133	−	0.822150i	4.45886	−	3.23955i	5.86756	+	4.26304i	1.54508	+	4.75528i	−1.47229	−	4.53124i	−2.26519	−	1.64576i	10.6672	−	7.75016i	1.04327	−	3.21086i	4.32230
31.5	0.849844	−	2.61555i	−5.86409	+	4.26051i	0.353259	+	0.256657i	1.54508	+	4.75528i	6.16003	+	18.9586i	24.9835	+	18.1516i	18.7709	−	13.6378i	7.89215	−	24.2895i	13.7508
31.6	1.50387	−	4.62843i	4.25544	−	3.09176i	−12.6886	−	9.21884i	1.54508	+	4.75528i	−7.91037	−	24.3456i	4.59294	+	3.33697i	−30.2534	+	21.9804i	0.206327	−	0.635008i	24.3331
36.1	−2.96806	+	2.15642i	−0.538187	−	1.65637i	1.68708	−	5.19231i	−4.04508	−	2.93893i	5.16920	+	3.75564i	2.95786	−	9.10335i	−2.88014	−	8.86415i	19.3895	−	14.0873i	18.3436
36.2	−1.81555	+	1.31908i	1.43526	+	4.41727i	−0.915867	+	2.81875i	−4.04508	−	2.93893i	−8.43250	−	6.12657i	−4.84499	+	14.9113i	−7.60317	−	23.4002i	4.39116	−	3.19036i	11.2207

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.c	even	5	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	55.4.g.b	✓	24
11.c	even	5	1	inner	55.4.g.b	✓	24
11.c	even	5	1		605.4.a.p		12
11.d	odd	10	1		605.4.a.t		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
55.4.g.b	✓	24	1.a	even	1	1	trivial
55.4.g.b	✓	24	11.c	even	5	1	inner
605.4.a.p		12	11.c	even	5	1
605.4.a.t		12	11.d	odd	10	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^24 - 6*T2^23 + 60*T2^22 - 290*T2^21 + 1977*T2^20 - 6286*T2^19 + 38260*T2^18 - 72348*T2^17 + 567141*T2^16 - 1015412*T2^15 + 6473188*T2^14 - 12822022*T2^13 + 82390849*T2^12 - 57597162*T2^11 + 391678388*T2^10 + 90536898*T2^9 + 2107778129*T2^8 - 1716651512*T2^7 + 8815373024*T2^6 + 3549754256*T2^5 + 31950031904*T2^4 + 19022470144*T2^3 + 19748673856*T2^2 + 15562344192*T2 + 9305303296