Newform orbit 108.5.j.a

• Label: 108.5.j.a
• Level: $108$
• Weight: $5$
• Character orbit: 108.j
• Analytic conductor: $11.164$
• Analytic rank: $0$
• Dimension: $420$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.1639560131\)
Analytic rank:	\(0\)
Dimension:	\(420\)
Relative dimension:	\(70\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 420 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−3.99762	−	0.137857i	5.81196	−	6.87176i	15.9620	+	1.10220i	−8.59701	−	48.7561i	−24.1814	+	26.6695i	32.6195	−	38.8744i	−63.6581	−	6.60665i	−13.4422	−	79.8768i	27.6463	+	196.094i
7.2	−3.98892	−	0.297585i	−6.50989	+	6.21461i	15.8229	+	2.37409i	−0.917019	−	5.20068i	27.8168	−	22.8523i	−5.99386	+	7.14320i	−62.4097	−	14.1787i	3.75733	−	80.9128i	2.11027	+	21.0179i
7.3	−3.96940	−	0.493852i	8.74142	+	2.14186i	15.5122	+	3.92059i	3.38596	+	19.2027i	−33.6404	−	12.8189i	59.9969	−	71.5016i	−59.6380	−	23.2231i	71.8248	+	37.4459i	−3.95691	−	77.8955i
7.4	−3.96518	−	0.526660i	6.87028	−	5.81371i	15.4453	+	4.17660i	4.27785	+	24.2609i	−30.3037	+	19.4341i	−42.2969	+	50.4075i	−59.0435	−	24.6954i	13.4016	−	79.8836i	−4.18518	−	98.4516i
7.5	−3.93992	+	0.690649i	−2.62931	−	8.60736i	15.0460	−	5.44221i	−0.426714	−	2.42002i	16.3040	+	32.0964i	−27.6515	+	32.9538i	−55.5215	+	31.8334i	−67.1734	+	45.2629i	3.35260	+	9.23997i
7.6	−3.93576	+	0.713980i	0.964020	+	8.94822i	14.9805	−	5.62011i	7.19320	+	40.7946i	−10.1830	−	34.5298i	−36.3946	+	43.3734i	−54.9469	+	32.8152i	−79.1413	+	17.2525i	−57.4373	−	155.422i
7.7	−3.88326	+	0.959324i	−8.67232	−	2.40643i	14.1594	−	7.45061i	−2.07418	−	11.7633i	35.9854	+	1.02521i	23.6467	−	28.1810i	−47.8370	+	42.5161i	69.4182	+	41.7386i	19.3394	+	43.6900i
7.8	−3.76323	−	1.35575i	4.63322	+	7.71578i	12.3239	+	10.2040i	−5.82341	−	33.0262i	−6.97519	−	35.3178i	−25.3950	+	30.2645i	−32.5435	−	55.1083i	−38.0666	+	71.4978i	−22.8605	+	132.180i
7.9	−3.62636	−	1.68805i	−8.87066	−	1.52033i	10.3010	+	12.2430i	7.76842	+	44.0569i	29.6018	+	20.4874i	7.01781	−	8.36350i	−16.6883	−	61.7859i	76.3772	+	26.9726i	46.1991	−	172.880i
7.10	−3.59139	+	1.76123i	8.67232	+	2.40643i	9.79617	−	12.6505i	−2.07418	−	11.7633i	−35.3839	+	6.63149i	−23.6467	+	28.1810i	−12.9015	+	62.6861i	69.4182	+	41.7386i	28.1670	+	38.5934i
7.11	−3.47391	+	1.98292i	−0.964020	−	8.94822i	8.13606	−	13.7770i	7.19320	+	40.7946i	21.0925	+	29.1737i	36.3946	−	43.3734i	−0.945324	+	63.9930i	−79.1413	+	17.2525i	−105.881	−	127.453i
7.12	−3.46210	+	2.00347i	2.62931	+	8.60736i	7.97224	−	13.8724i	−0.426714	−	2.42002i	−26.3475	−	24.5318i	27.6515	−	32.9538i	0.192185	+	63.9997i	−67.1734	+	45.2629i	6.32575	+	7.52343i
7.13	−3.43437	−	2.05063i	0.424142	−	8.99000i	7.58985	+	14.0852i	2.37776	+	13.4850i	−19.8918	+	30.0053i	18.1869	−	21.6743i	2.81722	−	63.9380i	−80.6402	−	7.62607i	19.4865	−	51.1883i
7.14	−3.38252	−	2.13508i	−5.83883	−	6.84895i	6.88287	+	14.4439i	−4.58821	−	26.0210i	5.12690	+	35.6331i	−28.7538	+	34.2674i	7.55742	−	63.5522i	−12.8162	+	79.9797i	−40.0372	+	97.8128i
7.15	−3.23826	−	2.34812i	−1.93752	+	8.78897i	4.97268	+	15.2076i	0.0896331	+	0.508335i	26.9118	−	23.9115i	39.0942	−	46.5907i	19.6065	−	60.9228i	−73.4920	−	34.0577i	0.903374	−	1.85659i
7.16	−2.97374	+	2.67523i	−5.81196	+	6.87176i	1.68632	−	15.9109i	−8.59701	−	48.7561i	−1.10023	−	35.9832i	−32.6195	+	38.8744i	37.5506	+	51.8262i	−13.4422	−	79.8768i	155.999	+	121.989i
7.17	−2.89182	−	2.76358i	8.96055	−	0.841750i	0.725269	+	15.9836i	−0.256732	−	1.45600i	−28.2386	−	22.3290i	−22.3218	+	26.6021i	42.0745	−	48.2259i	79.5829	−	15.0851i	−3.28135	+	4.91999i
7.18	−2.86440	+	2.79199i	6.50989	−	6.21461i	0.409598	−	15.9948i	−0.917019	−	5.20068i	−1.29583	+	35.9767i	5.99386	−	7.14320i	43.4839	+	46.9590i	3.75733	−	80.9128i	17.1469	+	12.3365i
7.19	−2.72329	+	2.92979i	−8.74142	−	2.14186i	−1.16736	−	15.9574i	3.38596	+	19.2027i	30.0807	−	19.7776i	−59.9969	+	71.5016i	49.9308	+	40.0364i	71.8248	+	37.4459i	−65.4810	−	42.3745i
7.20	−2.69897	+	2.95221i	−6.87028	+	5.81371i	−1.43111	−	15.9359i	4.27785	+	24.2609i	1.37940	−	35.9736i	42.2969	−	50.4075i	50.9086	+	38.7855i	13.4016	−	79.8836i	−83.1690	−	52.8503i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
27.e	even	9	1	inner
108.j	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	108.5.j.a	✓	420
4.b	odd	2	1	inner	108.5.j.a	✓	420
27.e	even	9	1	inner	108.5.j.a	✓	420
108.j	odd	18	1	inner	108.5.j.a	✓	420

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
108.5.j.a	✓	420	1.a	even	1	1	trivial
108.5.j.a	✓	420	4.b	odd	2	1	inner
108.5.j.a	✓	420	27.e	even	9	1	inner
108.5.j.a	✓	420	108.j	odd	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(108, [\chi])\).