Newform orbit 819.2.et.e

• Label: 819.2.et.e
• Level: $819$
• Weight: $2$
• Character orbit: 819.et
• Analytic conductor: $6.540$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.53974792554\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(18\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q + 12 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
136.1	−1.99280	+	1.99280i		0			−	5.94250i	−0.612692	+	2.28660i		0		−0.333036	+	2.62471i	7.85661	+	7.85661i		0		−3.33576	−	5.77770i
136.2	−1.68283	+	1.68283i		0			−	3.66380i	0.979703	−	3.65630i		0		2.62967	−	0.291230i	2.79989	+	2.79989i		0		4.50425	+	7.80158i
136.3	−1.67966	+	1.67966i		0			−	3.64248i	0.206512	−	0.770713i		0		−1.50859	−	2.17351i	2.75881	+	2.75881i		0		0.947664	+	1.64140i
136.4	−1.36554	+	1.36554i		0			−	1.72939i	−0.913161	+	3.40796i		0		2.17277	−	1.50965i	−0.369531	−	0.369531i		0		−3.40675	−	5.90066i
136.5	−1.28609	+	1.28609i		0			−	1.30808i	0.256278	−	0.956444i		0		−2.21931	+	1.44037i	−0.889876	−	0.889876i		0		0.900479	+	1.55968i
136.6	−0.690787	+	0.690787i		0				1.04563i	0.376327	−	1.40447i		0		−0.110664	−	2.64344i	−2.10388	−	2.10388i		0		0.710229	+	1.23015i
136.7	−0.634481	+	0.634481i		0				1.19487i	0.692371	−	2.58397i		0		1.60740	+	2.10149i	−2.02708	−	2.02708i		0		1.20018	+	2.07877i
136.8	−0.571833	+	0.571833i		0				1.34601i	−0.281618	+	1.05101i		0		2.64397	−	0.0969781i	−1.91336	−	1.91336i		0		−0.439965	−	0.762042i
136.9	−0.387463	+	0.387463i		0				1.69974i	−1.02055	+	3.80876i		0		−2.51619	−	0.817783i	−1.43352	−	1.43352i		0		−1.08033	−	1.87118i
136.10	0.387463	−	0.387463i		0				1.69974i	1.02055	−	3.80876i		0		−2.51619	−	0.817783i	1.43352	+	1.43352i		0		−1.08033	−	1.87118i
136.11	0.571833	−	0.571833i		0				1.34601i	0.281618	−	1.05101i		0		2.64397	−	0.0969781i	1.91336	+	1.91336i		0		−0.439965	−	0.762042i
136.12	0.634481	−	0.634481i		0				1.19487i	−0.692371	+	2.58397i		0		1.60740	+	2.10149i	2.02708	+	2.02708i		0		1.20018	+	2.07877i
136.13	0.690787	−	0.690787i		0				1.04563i	−0.376327	+	1.40447i		0		−0.110664	−	2.64344i	2.10388	+	2.10388i		0		0.710229	+	1.23015i
136.14	1.28609	−	1.28609i		0			−	1.30808i	−0.256278	+	0.956444i		0		−2.21931	+	1.44037i	0.889876	+	0.889876i		0		0.900479	+	1.55968i
136.15	1.36554	−	1.36554i		0			−	1.72939i	0.913161	−	3.40796i		0		2.17277	−	1.50965i	0.369531	+	0.369531i		0		−3.40675	−	5.90066i
136.16	1.67966	−	1.67966i		0			−	3.64248i	−0.206512	+	0.770713i		0		−1.50859	−	2.17351i	−2.75881	−	2.75881i		0		0.947664	+	1.64140i
136.17	1.68283	−	1.68283i		0			−	3.66380i	−0.979703	+	3.65630i		0		2.62967	−	0.291230i	−2.79989	−	2.79989i		0		4.50425	+	7.80158i
136.18	1.99280	−	1.99280i		0			−	5.94250i	0.612692	−	2.28660i		0		−0.333036	+	2.62471i	−7.85661	−	7.85661i		0		−3.33576	−	5.77770i
145.1	−1.85075	+	1.85075i		0			−	4.85057i	2.17263	−	0.582154i		0		−2.53443	−	0.759392i	5.27570	+	5.27570i		0		−2.94358	+	5.09842i
145.2	−1.80157	+	1.80157i		0			−	4.49134i	−3.37206	+	0.903542i		0		−0.106255	−	2.64362i	4.48833	+	4.48833i		0		4.44722	−	7.70282i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
91.ba	even	12	1	inner
273.bs	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	819.2.et.e	✓	72
3.b	odd	2	1	inner	819.2.et.e	✓	72
7.d	odd	6	1		819.2.gh.e	yes	72
13.f	odd	12	1		819.2.gh.e	yes	72
21.g	even	6	1		819.2.gh.e	yes	72
39.k	even	12	1		819.2.gh.e	yes	72
91.ba	even	12	1	inner	819.2.et.e	✓	72
273.bs	odd	12	1	inner	819.2.et.e	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
819.2.et.e	✓	72	1.a	even	1	1	trivial
819.2.et.e	✓	72	3.b	odd	2	1	inner
819.2.et.e	✓	72	91.ba	even	12	1	inner
819.2.et.e	✓	72	273.bs	odd	12	1	inner
819.2.gh.e	yes	72	7.d	odd	6	1
819.2.gh.e	yes	72	13.f	odd	12	1
819.2.gh.e	yes	72	21.g	even	6	1
819.2.gh.e	yes	72	39.k	even	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^72 + 294*T2^68 + 37671*T2^64 + 2775764*T2^60 + 130715299*T2^56 + 4137253512*T2^52 + 90181133637*T2^48 + 1365768298194*T2^44 + 14333900160426*T2^40 + 102898351722770*T2^36 + 493302675214149*T2^32 + 1524922948955412*T2^28 + 2910163237112873*T2^24 + 3283186803122594*T2^20 + 2127358066557255*T2^16 + 751531941275270*T2^12 + 126545517580762*T2^8 + 6740357597640*T2^4 + 7354949121