Newform orbit 832.2.i.e

• Label: 832.2.i.e
• Level: $832$
• Weight: $2$
• Character orbit: 832.i
• Analytic conductor: $6.644$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.64355344817\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-3}) \)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 26)
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.

\(f(q)\)	\(=\)	\( q + q^{5} - 4 \zeta_{6} q^{7} + 3 \zeta_{6} q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} - 4 q^{7} + 3 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/832\mathbb{Z}\right)^\times\).

\(n\)	\(261\)	\(703\)	\(769\)
\(\chi(n)\)	\(1\)	\(1\)	\(-\zeta_{6}\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

321.1

0.500000	+	0.866025i
0.500000	−	0.866025i

0

0

0

1.00000

0

−2.00000

−

3.46410i

0

1.50000

+

2.59808i

0

705.1

0

0

0

1.00000

0

−2.00000

+

3.46410i

0

1.50000

−

2.59808i

0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	832.2.i.e		2
4.b	odd	2	1		832.2.i.f		2
8.b	even	2	1		26.2.c.a	✓	2
8.d	odd	2	1		208.2.i.b		2
13.c	even	3	1	inner	832.2.i.e		2
24.f	even	2	1		1872.2.t.k		2
24.h	odd	2	1		234.2.h.c		2
40.f	even	2	1		650.2.e.c		2
40.i	odd	4	2		650.2.o.c		4
52.j	odd	6	1		832.2.i.f		2
56.h	odd	2	1		1274.2.g.a		2
56.j	odd	6	1		1274.2.e.m		2
56.j	odd	6	1		1274.2.h.a		2
56.p	even	6	1		1274.2.e.n		2
56.p	even	6	1		1274.2.h.b		2
104.e	even	2	1		338.2.c.e		2
104.j	odd	4	2		338.2.e.b		4
104.n	odd	6	1		208.2.i.b		2
104.n	odd	6	1		2704.2.a.h		1
104.p	odd	6	1		2704.2.a.i		1
104.r	even	6	1		26.2.c.a	✓	2
104.r	even	6	1		338.2.a.e		1
104.s	even	6	1		338.2.a.c		1
104.s	even	6	1		338.2.c.e		2
104.u	even	12	2		2704.2.f.g		2
104.x	odd	12	2		338.2.b.b		2
104.x	odd	12	2		338.2.e.b		4
312.bg	odd	6	1		3042.2.a.k		1
312.bh	odd	6	1		234.2.h.c		2
312.bh	odd	6	1		3042.2.a.e		1
312.bn	even	6	1		1872.2.t.k		2
312.bo	even	12	2		3042.2.b.e		2
520.bp	even	6	1		8450.2.a.s		1
520.bv	even	6	1		650.2.e.c		2
520.bv	even	6	1		8450.2.a.f		1
520.cq	odd	12	2		650.2.o.c		4
728.bg	even	6	1		1274.2.e.n		2
728.bq	odd	6	1		1274.2.h.a		2
728.ce	odd	6	1		1274.2.g.a		2
728.cw	even	6	1		1274.2.h.b		2
728.de	odd	6	1		1274.2.e.m		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
26.2.c.a	✓	2	8.b	even	2	1
26.2.c.a	✓	2	104.r	even	6	1
208.2.i.b		2	8.d	odd	2	1
208.2.i.b		2	104.n	odd	6	1
234.2.h.c		2	24.h	odd	2	1
234.2.h.c		2	312.bh	odd	6	1
338.2.a.c		1	104.s	even	6	1
338.2.a.e		1	104.r	even	6	1
338.2.b.b		2	104.x	odd	12	2
338.2.c.e		2	104.e	even	2	1
338.2.c.e		2	104.s	even	6	1
338.2.e.b		4	104.j	odd	4	2
338.2.e.b		4	104.x	odd	12	2
650.2.e.c		2	40.f	even	2	1
650.2.e.c		2	520.bv	even	6	1
650.2.o.c		4	40.i	odd	4	2
650.2.o.c		4	520.cq	odd	12	2
832.2.i.e		2	1.a	even	1	1	trivial
832.2.i.e		2	13.c	even	3	1	inner
832.2.i.f		2	4.b	odd	2	1
832.2.i.f		2	52.j	odd	6	1
1274.2.e.m		2	56.j	odd	6	1
1274.2.e.m		2	728.de	odd	6	1
1274.2.e.n		2	56.p	even	6	1
1274.2.e.n		2	728.bg	even	6	1
1274.2.g.a		2	56.h	odd	2	1
1274.2.g.a		2	728.ce	odd	6	1
1274.2.h.a		2	56.j	odd	6	1
1274.2.h.a		2	728.bq	odd	6	1
1274.2.h.b		2	56.p	even	6	1
1274.2.h.b		2	728.cw	even	6	1
1872.2.t.k		2	24.f	even	2	1
1872.2.t.k		2	312.bn	even	6	1
2704.2.a.h		1	104.n	odd	6	1
2704.2.a.i		1	104.p	odd	6	1
2704.2.f.g		2	104.u	even	12	2
3042.2.a.e		1	312.bh	odd	6	1
3042.2.a.k		1	312.bg	odd	6	1
3042.2.b.e		2	312.bo	even	12	2
8450.2.a.f		1	520.bv	even	6	1
8450.2.a.s		1	520.bp	even	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(832, [\chi])\):

\( T_{3} \)

\( T_{5} - 1 \)

\( T_{7}^{2} + 4T_{7} + 16 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( (T - 1)^{2} \)
$7$	\( T^{2} + 4T + 16 \)
$11$	\( T^{2} - 4T + 16 \)