Newform orbit 891.2.e.l

• Label: 891.2.e.l
• Level: $891$
• Weight: $2$
• Character orbit: 891.e
• Analytic conductor: $7.115$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.11467082010\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-3}) \)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a primitive root of unity \(\zeta_{6}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q + ( - 2 \zeta_{6} + 2) q^{2} - 2 \zeta_{6} q^{4} + 2 \zeta_{6} q^{5} + (\zeta_{6} - 1) q^{7} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\)	\(244\)	\(650\)
\(\chi(n)\)	\(1\)	\(-\zeta_{6}\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

298.1

0.500000	+	0.866025i
0.500000	−	0.866025i

1.00000

−

1.73205i

0

−1.00000

−

1.73205i

1.00000

+

1.73205i

0

−0.500000

+

0.866025i

0

0

4.00000

595.1

1.00000

+

1.73205i

0

−1.00000

+

1.73205i

1.00000

−

1.73205i

0

−0.500000

−

0.866025i

0

0

4.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	891.2.e.l		2
3.b	odd	2	1		891.2.e.a		2
9.c	even	3	1		297.2.a.a	✓	1
9.c	even	3	1	inner	891.2.e.l		2
9.d	odd	6	1		297.2.a.d	yes	1
9.d	odd	6	1		891.2.e.a		2
36.f	odd	6	1		4752.2.a.c		1
36.h	even	6	1		4752.2.a.o		1
45.h	odd	6	1		7425.2.a.b		1
45.j	even	6	1		7425.2.a.u		1
99.g	even	6	1		3267.2.a.a		1
99.h	odd	6	1		3267.2.a.k		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
297.2.a.a	✓	1	9.c	even	3	1
297.2.a.d	yes	1	9.d	odd	6	1
891.2.e.a		2	3.b	odd	2	1
891.2.e.a		2	9.d	odd	6	1
891.2.e.l		2	1.a	even	1	1	trivial
891.2.e.l		2	9.c	even	3	1	inner
3267.2.a.a		1	99.g	even	6	1
3267.2.a.k		1	99.h	odd	6	1
4752.2.a.c		1	36.f	odd	6	1
4752.2.a.o		1	36.h	even	6	1
7425.2.a.b		1	45.h	odd	6	1
7425.2.a.u		1	45.j	even	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(891, [\chi])\):

\( T_{2}^{2} - 2T_{2} + 4 \)

\( T_{5}^{2} - 2T_{5} + 4 \)

\( T_{7}^{2} + T_{7} + 1 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} - 2T + 4 \)
$3$	\( T^{2} \)
$5$	\( T^{2} - 2T + 4 \)
$7$	\( T^{2} + T + 1 \)
$11$	\( T^{2} + T + 1 \)