Newform orbit 1792.2.b.a

• Label: 1792.2.b.a
• Level: $1792$
• Weight: $2$
• Character orbit: 1792.b
• Analytic conductor: $14.309$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.3091920422\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-1}) \)
Defining polynomial:	\( x^{2} + 1 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 2 \)
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2i\). We also show the integral \(q\)-expansion of the trace form.

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\)	\(1023\)	\(1025\)	\(1541\)
\(\chi(n)\)	\(1\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

897.1

	−	1.00000i
		1.00000i

0

−

2.00000i

0

−

4.00000i

0

−1.00000

0

−1.00000

0

897.2

0

2.00000i

0

4.00000i

0

−1.00000

0

−1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1792.2.b.a		2
4.b	odd	2	1		1792.2.b.h		2
8.b	even	2	1	inner	1792.2.b.a		2
8.d	odd	2	1		1792.2.b.h		2
16.e	even	4	1		56.2.a.b	✓	1
16.e	even	4	1		448.2.a.c		1
16.f	odd	4	1		112.2.a.a		1
16.f	odd	4	1		448.2.a.h		1
48.i	odd	4	1		504.2.a.h		1
48.i	odd	4	1		4032.2.a.d		1
48.k	even	4	1		1008.2.a.m		1
48.k	even	4	1		4032.2.a.a		1
80.i	odd	4	1		1400.2.g.b		2
80.j	even	4	1		2800.2.g.g		2
80.k	odd	4	1		2800.2.a.bd		1
80.q	even	4	1		1400.2.a.a		1
80.s	even	4	1		2800.2.g.g		2
80.t	odd	4	1		1400.2.g.b		2
112.j	even	4	1		784.2.a.i		1
112.j	even	4	1		3136.2.a.c		1
112.l	odd	4	1		392.2.a.b		1
112.l	odd	4	1		3136.2.a.w		1
112.u	odd	12	2		784.2.i.j		2
112.v	even	12	2		784.2.i.b		2
112.w	even	12	2		392.2.i.a		2
112.x	odd	12	2		392.2.i.e		2
176.l	odd	4	1		6776.2.a.h		1
208.p	even	4	1		9464.2.a.h		1
336.v	odd	4	1		7056.2.a.c		1
336.y	even	4	1		3528.2.a.b		1
336.bo	even	12	2		3528.2.s.ba		2
336.bt	odd	12	2		3528.2.s.a		2
560.bf	odd	4	1		9800.2.a.bj		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
56.2.a.b	✓	1	16.e	even	4	1
112.2.a.a		1	16.f	odd	4	1
392.2.a.b		1	112.l	odd	4	1
392.2.i.a		2	112.w	even	12	2
392.2.i.e		2	112.x	odd	12	2
448.2.a.c		1	16.e	even	4	1
448.2.a.h		1	16.f	odd	4	1
504.2.a.h		1	48.i	odd	4	1
784.2.a.i		1	112.j	even	4	1
784.2.i.b		2	112.v	even	12	2
784.2.i.j		2	112.u	odd	12	2
1008.2.a.m		1	48.k	even	4	1
1400.2.a.a		1	80.q	even	4	1
1400.2.g.b		2	80.i	odd	4	1
1400.2.g.b		2	80.t	odd	4	1
1792.2.b.a		2	1.a	even	1	1	trivial
1792.2.b.a		2	8.b	even	2	1	inner
1792.2.b.h		2	4.b	odd	2	1
1792.2.b.h		2	8.d	odd	2	1
2800.2.a.bd		1	80.k	odd	4	1
2800.2.g.g		2	80.j	even	4	1
2800.2.g.g		2	80.s	even	4	1
3136.2.a.c		1	112.j	even	4	1
3136.2.a.w		1	112.l	odd	4	1
3528.2.a.b		1	336.y	even	4	1
3528.2.s.a		2	336.bt	odd	12	2
3528.2.s.ba		2	336.bo	even	12	2
4032.2.a.a		1	48.k	even	4	1
4032.2.a.d		1	48.i	odd	4	1
6776.2.a.h		1	176.l	odd	4	1
7056.2.a.c		1	336.v	odd	4	1
9464.2.a.h		1	208.p	even	4	1
9800.2.a.bj		1	560.bf	odd	4	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1792, [\chi])\):

\( T_{3}^{2} + 4 \)

\( T_{5}^{2} + 16 \)

\( T_{11} \)

\( T_{23} + 8 \)

\( T_{31} - 4 \)

Hecke characteristic polynomials

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