Newform orbit 54.4.e.a

• Label: 54.4.e.a
• Level: $54$
• Weight: $4$
• Character orbit: 54.e
• Analytic conductor: $3.186$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.18610314031\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(4\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{5} - 18 q^{6} - 33 q^{7} - 96 q^{8} + 54 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−1.87939	+	0.684040i	−4.81994	−	1.94118i	3.06418	−	2.57115i	0.203469	+	1.15393i	10.3864	+	0.351184i	19.9691	+	16.7561i	−4.00000	+	6.92820i	19.4637	+	18.7127i	−1.17173	−	2.02949i
7.2	−1.87939	+	0.684040i	−0.530916	−	5.16896i	3.06418	−	2.57115i	1.18374	+	6.71331i	4.53357	+	9.35130i	−25.7220	−	21.5833i	−4.00000	+	6.92820i	−26.4363	+	5.48857i	−6.81687	−	11.8072i
7.3	−1.87939	+	0.684040i	2.43378	+	4.59094i	3.06418	−	2.57115i	1.31542	+	7.46011i	−7.71439	−	6.96335i	−2.90083	−	2.43409i	−4.00000	+	6.92820i	−15.1535	+	22.3466i	−7.57519	−	13.1206i
7.4	−1.87939	+	0.684040i	5.14376	−	0.735997i	3.06418	−	2.57115i	−2.50669	−	14.2161i	−9.16366	+	4.90176i	0.855575	+	0.717913i	−4.00000	+	6.92820i	25.9166	−	7.57159i	14.4354	+	25.0029i
13.1	0.347296	+	1.96962i	−4.52643	+	2.55175i	−3.75877	+	1.36808i	−5.66862	−	4.75653i	−6.59798	−	8.02911i	−11.1935	−	4.07412i	−4.00000	−	6.92820i	13.9771	−	23.1006i	7.39985	−	12.8169i
13.2	0.347296	+	1.96962i	−1.09637	−	5.07917i	−3.75877	+	1.36808i	−12.8013	−	10.7416i	9.62325	−	3.92341i	−9.76778	−	3.55518i	−4.00000	−	6.92820i	−24.5959	+	11.1373i	16.7110	−	28.9442i
13.3	0.347296	+	1.96962i	2.36769	+	4.62537i	−3.75877	+	1.36808i	5.41266	+	4.54176i	−8.28791	+	6.26981i	−4.71753	−	1.71704i	−4.00000	−	6.92820i	−15.7881	+	21.9029i	−7.06572	+	12.2382i
13.4	0.347296	+	1.96962i	4.43991	−	2.69949i	−3.75877	+	1.36808i	3.46830	+	2.91025i	6.85891	+	7.80739i	22.9979	+	8.37056i	−4.00000	−	6.92820i	12.4256	−	23.9709i	−4.52754	+	7.84193i
25.1	0.347296	−	1.96962i	−4.52643	−	2.55175i	−3.75877	−	1.36808i	−5.66862	+	4.75653i	−6.59798	+	8.02911i	−11.1935	+	4.07412i	−4.00000	+	6.92820i	13.9771	+	23.1006i	7.39985	+	12.8169i
25.2	0.347296	−	1.96962i	−1.09637	+	5.07917i	−3.75877	−	1.36808i	−12.8013	+	10.7416i	9.62325	+	3.92341i	−9.76778	+	3.55518i	−4.00000	+	6.92820i	−24.5959	−	11.1373i	16.7110	+	28.9442i
25.3	0.347296	−	1.96962i	2.36769	−	4.62537i	−3.75877	−	1.36808i	5.41266	−	4.54176i	−8.28791	−	6.26981i	−4.71753	+	1.71704i	−4.00000	+	6.92820i	−15.7881	−	21.9029i	−7.06572	−	12.2382i
25.4	0.347296	−	1.96962i	4.43991	+	2.69949i	−3.75877	−	1.36808i	3.46830	−	2.91025i	6.85891	−	7.80739i	22.9979	−	8.37056i	−4.00000	+	6.92820i	12.4256	+	23.9709i	−4.52754	−	7.84193i
31.1	−1.87939	−	0.684040i	−4.81994	+	1.94118i	3.06418	+	2.57115i	0.203469	−	1.15393i	10.3864	−	0.351184i	19.9691	−	16.7561i	−4.00000	−	6.92820i	19.4637	−	18.7127i	−1.17173	+	2.02949i
31.2	−1.87939	−	0.684040i	−0.530916	+	5.16896i	3.06418	+	2.57115i	1.18374	−	6.71331i	4.53357	−	9.35130i	−25.7220	+	21.5833i	−4.00000	−	6.92820i	−26.4363	−	5.48857i	−6.81687	+	11.8072i
31.3	−1.87939	−	0.684040i	2.43378	−	4.59094i	3.06418	+	2.57115i	1.31542	−	7.46011i	−7.71439	+	6.96335i	−2.90083	+	2.43409i	−4.00000	−	6.92820i	−15.1535	−	22.3466i	−7.57519	+	13.1206i
31.4	−1.87939	−	0.684040i	5.14376	+	0.735997i	3.06418	+	2.57115i	−2.50669	+	14.2161i	−9.16366	−	4.90176i	0.855575	−	0.717913i	−4.00000	−	6.92820i	25.9166	+	7.57159i	14.4354	−	25.0029i
43.1	1.53209	+	1.28558i	−4.93920	−	1.61377i	0.694593	+	3.93923i	18.7075	+	6.80898i	−5.49268	−	8.82216i	−3.26433	+	18.5129i	−4.00000	+	6.92820i	21.7915	+	15.9415i	19.9081	+	34.4819i
43.2	1.53209	+	1.28558i	−4.87472	+	1.79919i	0.694593	+	3.93923i	−19.8413	−	7.22164i	−9.78150	−	3.51031i	−3.38399	+	19.1916i	−4.00000	+	6.92820i	20.5258	−	17.5411i	−21.1147	−	36.5717i
43.3	1.53209	+	1.28558i	1.79748	+	4.87535i	0.694593	+	3.93923i	1.07676	+	0.391909i	−3.51374	+	9.78027i	0.470326	−	2.66735i	−4.00000	+	6.92820i	−20.5381	+	17.5267i	1.14586	+	1.98470i
43.4	1.53209	+	1.28558i	4.60498	−	2.40711i	0.694593	+	3.93923i	3.45007	+	1.25572i	10.1498	+	2.23213i	0.157049	−	0.890672i	−4.00000	+	6.92820i	15.4116	−	22.1694i	3.67149	+	6.35921i

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	54.4.e.a	✓	24
3.b	odd	2	1		162.4.e.a		24
27.e	even	9	1	inner	54.4.e.a	✓	24
27.e	even	9	1		1458.4.a.h		12
27.f	odd	18	1		162.4.e.a		24
27.f	odd	18	1		1458.4.a.e		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
54.4.e.a	✓	24	1.a	even	1	1	trivial
54.4.e.a	✓	24	27.e	even	9	1	inner
162.4.e.a		24	3.b	odd	2	1
162.4.e.a		24	27.f	odd	18	1
1458.4.a.e		12	27.f	odd	18	1
1458.4.a.h		12	27.e	even	9	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 12*T5^23 - 360*T5^22 - 6699*T5^21 + 31221*T5^20 + 1138725*T5^19 + 32801526*T5^18 + 187511760*T5^17 + 1422469026*T5^16 - 40147364502*T5^15 + 1046335291083*T5^14 - 11976030471159*T5^13 + 107514187034643*T5^12 - 677801835183474*T5^11 + 4690657372989582*T5^10 - 38205564519282363*T5^9 + 318983007070137996*T5^8 - 2218172364337507722*T5^7 + 11489749303921898922*T5^6 - 40907865708628641396*T5^5 + 95132053304239088196*T5^4 - 141573605742504384885*T5^3 + 147055468139466629688*T5^2 - 103911042799093004019*T5 + 37336980204259623801