Newform orbit 27.4.e.a

• Label: 27.4.e.a
• Level: $27$
• Weight: $4$
• Character orbit: 27.e
• Analytic conductor: $1.593$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.59305157015\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(8\) over \(\Q(\zeta_{9})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \)

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	−4.97861	−	1.81207i	−3.67671	−	3.67176i	15.3746	+	12.9008i	−1.82513	+	10.3508i	11.6515	+	24.9427i	−5.92244	+	4.96952i	−31.9745	−	55.3815i	0.0364268	+	27.0000i	27.8430	−	48.2255i
4.2	−4.05233	−	1.47493i	4.37853	+	2.79794i	8.11761	+	6.81148i	3.22691	−	18.3007i	−13.6165	−	17.7962i	14.4087	−	12.0903i	−5.59920	−	9.69809i	11.3431	+	24.5017i	−40.0687	+	69.4011i
4.3	−2.12171	−	0.772239i	−0.789571	+	5.13581i	−2.22306	−	1.86537i	−3.33920	+	18.9376i	5.64131	−	10.2870i	0.500915	−	0.420318i	12.3077	+	21.3175i	−25.7532	−	8.11018i	21.7091	−	37.6013i
4.4	−0.982993	−	0.357780i	−5.19600	−	0.0395600i	−5.29009	−	4.43891i	2.68017	−	15.2000i	5.09348	+	1.89791i	−18.0349	+	15.1331i	7.79628	+	13.5036i	26.9969	+	0.411107i	−8.07284	+	13.9826i
4.5	−0.932125	−	0.339266i	1.23404	−	5.04749i	−5.37460	−	4.50982i	0.0250883	−	0.142283i	−2.86272	+	4.28623i	19.4381	−	16.3105i	7.44756	+	12.8996i	−23.9543	−	12.4576i	−0.0716572	+	0.124114i
4.6	1.82340	+	0.663664i	5.12138	+	0.878355i	−3.24401	−	2.72205i	−0.470388	+	2.66770i	8.75540	+	5.00047i	−9.12942	+	7.66050i	−11.8703	−	20.5600i	25.4570	+	8.99678i	−2.62817	+	4.55212i
4.7	3.53135	+	1.28531i	−2.46998	+	4.57157i	4.69008	+	3.93544i	1.06026	−	6.01302i	−14.5982	+	12.9691i	13.2194	−	11.0924i	−3.52788	−	6.11047i	−14.7984	−	22.5833i	11.4727	−	19.8713i
4.8	4.06758	+	1.48048i	−1.65472	−	4.92564i	8.22505	+	6.90164i	−0.745703	+	4.22909i	0.561612	−	22.4852i	−15.6540	+	13.1353i	5.92381	+	10.2603i	−21.5238	+	16.3011i	−9.29428	+	16.0982i
7.1	−4.97861	+	1.81207i	−3.67671	+	3.67176i	15.3746	−	12.9008i	−1.82513	−	10.3508i	11.6515	−	24.9427i	−5.92244	−	4.96952i	−31.9745	+	55.3815i	0.0364268	−	27.0000i	27.8430	+	48.2255i
7.2	−4.05233	+	1.47493i	4.37853	−	2.79794i	8.11761	−	6.81148i	3.22691	+	18.3007i	−13.6165	+	17.7962i	14.4087	+	12.0903i	−5.59920	+	9.69809i	11.3431	−	24.5017i	−40.0687	−	69.4011i
7.3	−2.12171	+	0.772239i	−0.789571	−	5.13581i	−2.22306	+	1.86537i	−3.33920	−	18.9376i	5.64131	+	10.2870i	0.500915	+	0.420318i	12.3077	−	21.3175i	−25.7532	+	8.11018i	21.7091	+	37.6013i
7.4	−0.982993	+	0.357780i	−5.19600	+	0.0395600i	−5.29009	+	4.43891i	2.68017	+	15.2000i	5.09348	−	1.89791i	−18.0349	−	15.1331i	7.79628	−	13.5036i	26.9969	−	0.411107i	−8.07284	−	13.9826i
7.5	−0.932125	+	0.339266i	1.23404	+	5.04749i	−5.37460	+	4.50982i	0.0250883	+	0.142283i	−2.86272	−	4.28623i	19.4381	+	16.3105i	7.44756	−	12.8996i	−23.9543	+	12.4576i	−0.0716572	−	0.124114i
7.6	1.82340	−	0.663664i	5.12138	−	0.878355i	−3.24401	+	2.72205i	−0.470388	−	2.66770i	8.75540	−	5.00047i	−9.12942	−	7.66050i	−11.8703	+	20.5600i	25.4570	−	8.99678i	−2.62817	−	4.55212i
7.7	3.53135	−	1.28531i	−2.46998	−	4.57157i	4.69008	−	3.93544i	1.06026	+	6.01302i	−14.5982	−	12.9691i	13.2194	+	11.0924i	−3.52788	+	6.11047i	−14.7984	+	22.5833i	11.4727	+	19.8713i
7.8	4.06758	−	1.48048i	−1.65472	+	4.92564i	8.22505	−	6.90164i	−0.745703	−	4.22909i	0.561612	+	22.4852i	−15.6540	−	13.1353i	5.92381	−	10.2603i	−21.5238	−	16.3011i	−9.29428	−	16.0982i
13.1	−0.874714	−	4.96075i	2.71299	−	4.43167i	−16.3263	+	5.94230i	11.9326	+	10.0126i	−24.3575	−	9.58200i	−5.29732	−	1.92807i	23.6100	+	40.8938i	−12.2794	−	24.0461i	39.2325	−	67.9527i
13.2	−0.592608	−	3.36085i	−5.15968	−	0.614572i	−3.42657	+	1.24717i	−8.41296	−	7.05931i	0.992184	+	17.7051i	4.14024	+	1.50692i	−7.42861	−	12.8667i	26.2446	+	6.34199i	−18.7397	+	32.4581i
13.3	−0.404735	−	2.29536i	4.52897	+	2.54724i	2.41266	−	0.878135i	−4.78113	−	4.01185i	4.01380	−	11.4266i	2.53990	+	0.924448i	−12.3152	−	21.3306i	14.0232	+	23.0727i	−7.27356	+	12.5982i
13.4	−0.0518956	−	0.294314i	−2.82128	+	4.36353i	7.43361	−	2.70561i	15.3604	+	12.8889i	1.43066	+	0.603897i	−20.1945	−	7.35018i	−2.37749	−	4.11794i	−11.0807	−	24.6215i	2.99626	−	5.18968i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
27.e	even	9	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	27.4.e.a	✓	48
3.b	odd	2	1		81.4.e.a		48
9.c	even	3	1		243.4.e.c		48
9.c	even	3	1		243.4.e.d		48
9.d	odd	6	1		243.4.e.a		48
9.d	odd	6	1		243.4.e.b		48
27.e	even	9	1	inner	27.4.e.a	✓	48
27.e	even	9	1		243.4.e.c		48
27.e	even	9	1		243.4.e.d		48
27.e	even	9	1		729.4.a.d		24
27.f	odd	18	1		81.4.e.a		48
27.f	odd	18	1		243.4.e.a		48
27.f	odd	18	1		243.4.e.b		48
27.f	odd	18	1		729.4.a.c		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
27.4.e.a	✓	48	1.a	even	1	1	trivial
27.4.e.a	✓	48	27.e	even	9	1	inner
81.4.e.a		48	3.b	odd	2	1
81.4.e.a		48	27.f	odd	18	1
243.4.e.a		48	9.d	odd	6	1
243.4.e.a		48	27.f	odd	18	1
243.4.e.b		48	9.d	odd	6	1
243.4.e.b		48	27.f	odd	18	1
243.4.e.c		48	9.c	even	3	1
243.4.e.c		48	27.e	even	9	1
243.4.e.d		48	9.c	even	3	1
243.4.e.d		48	27.e	even	9	1
729.4.a.c		24	27.f	odd	18	1
729.4.a.d		24	27.e	even	9	1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(27, [\chi])\).