Newform orbit 1792.2.b.i

• Label: 1792.2.b.i
• Level: $1792$
• Weight: $2$
• Character orbit: 1792.b
• Analytic conductor: $14.309$
• Analytic rank: $0$
• Dimension: $2$
• 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:	\(\Z[a_1, \ldots, a_{5}]\)
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 - b * q^5 + q^7 + 3 * q^9 + 2*b * q^11 + b * q^13 - 6 * q^17 + 4*b * q^19 + q^25 + 3*b * q^29 + 8 * q^31 - b * q^35 + b * q^37 - 2 * q^41 + 2*b * q^43 - 3*b * q^45 - 8 * q^47 + q^49 - 3*b * q^53 + 8 * q^55 - 3*b * q^61 + 3 * q^63 + 4 * q^65 - 2*b * q^67 + 8 * q^71 - 10 * q^73 + 2*b * q^77 + 16 * q^79 + 9 * q^81 + 4*b * q^83 + 6*b * q^85 + 6 * q^89 + b * q^91 + 16 * q^95 - 6 * q^97 + 6*b * q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{7} + 6 q^{9} - 12 q^{17} + 2 q^{25} + 16 q^{31} - 4 q^{41} - 16 q^{47} + 2 q^{49} + 16 q^{55} + 6 q^{63} + 8 q^{65} + 16 q^{71} - 20 q^{73} + 32 q^{79} + 18 q^{81} + 12 q^{89} + 32 q^{95} - 12 q^{97}+O(q^{100}) \)

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

0

0

−

2.00000i

0

1.00000

0

3.00000

0

897.2

0

0

0

2.00000i

0

1.00000

0

3.00000

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.i		2
4.b	odd	2	1		1792.2.b.d		2
8.b	even	2	1	inner	1792.2.b.i		2
8.d	odd	2	1		1792.2.b.d		2
16.e	even	4	1		56.2.a.a	✓	1
16.e	even	4	1		448.2.a.d		1
16.f	odd	4	1		112.2.a.b		1
16.f	odd	4	1		448.2.a.e		1
48.i	odd	4	1		504.2.a.c		1
48.i	odd	4	1		4032.2.a.bb		1
48.k	even	4	1		1008.2.a.d		1
48.k	even	4	1		4032.2.a.bk		1
80.i	odd	4	1		1400.2.g.g		2
80.j	even	4	1		2800.2.g.p		2
80.k	odd	4	1		2800.2.a.p		1
80.q	even	4	1		1400.2.a.g		1
80.s	even	4	1		2800.2.g.p		2
80.t	odd	4	1		1400.2.g.g		2
112.j	even	4	1		784.2.a.e		1
112.j	even	4	1		3136.2.a.p		1
112.l	odd	4	1		392.2.a.d		1
112.l	odd	4	1		3136.2.a.q		1
112.u	odd	12	2		784.2.i.e		2
112.v	even	12	2		784.2.i.g		2
112.w	even	12	2		392.2.i.c		2
112.x	odd	12	2		392.2.i.d		2
176.l	odd	4	1		6776.2.a.g		1
208.p	even	4	1		9464.2.a.c		1
336.v	odd	4	1		7056.2.a.bo		1
336.y	even	4	1		3528.2.a.x		1
336.bo	even	12	2		3528.2.s.e		2
336.bt	odd	12	2		3528.2.s.t		2
560.bf	odd	4	1		9800.2.a.u		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
56.2.a.a	✓	1	16.e	even	4	1
112.2.a.b		1	16.f	odd	4	1
392.2.a.d		1	112.l	odd	4	1
392.2.i.c		2	112.w	even	12	2
392.2.i.d		2	112.x	odd	12	2
448.2.a.d		1	16.e	even	4	1
448.2.a.e		1	16.f	odd	4	1
504.2.a.c		1	48.i	odd	4	1
784.2.a.e		1	112.j	even	4	1
784.2.i.e		2	112.u	odd	12	2
784.2.i.g		2	112.v	even	12	2
1008.2.a.d		1	48.k	even	4	1
1400.2.a.g		1	80.q	even	4	1
1400.2.g.g		2	80.i	odd	4	1
1400.2.g.g		2	80.t	odd	4	1
1792.2.b.d		2	4.b	odd	2	1
1792.2.b.d		2	8.d	odd	2	1
1792.2.b.i		2	1.a	even	1	1	trivial
1792.2.b.i		2	8.b	even	2	1	inner
2800.2.a.p		1	80.k	odd	4	1
2800.2.g.p		2	80.j	even	4	1
2800.2.g.p		2	80.s	even	4	1
3136.2.a.p		1	112.j	even	4	1
3136.2.a.q		1	112.l	odd	4	1
3528.2.a.x		1	336.y	even	4	1
3528.2.s.e		2	336.bo	even	12	2
3528.2.s.t		2	336.bt	odd	12	2
4032.2.a.bb		1	48.i	odd	4	1
4032.2.a.bk		1	48.k	even	4	1
6776.2.a.g		1	176.l	odd	4	1
7056.2.a.bo		1	336.v	odd	4	1
9464.2.a.c		1	208.p	even	4	1
9800.2.a.u		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 \(S_{2}^{\mathrm{new}}(1792, [\chi])\):

\( T_{3} \)

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

\( T_{11}^{2} + 16 \)

\( T_{23} \)

\( T_{31} - 8 \)

Hecke characteristic polynomials

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