Newform orbit 192.2.a.c

• Label: 192.2.a.c
• Level: $192$
• Weight: $2$
• Character orbit: 192.a
• Self dual: yes
• Analytic conductor: $1.533$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.53312771881\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 96)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{3} - 2 q^{5} + 4 q^{7} + q^{9}+O(q^{10}) \)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

0

0

1.00000

0

−2.00000

0

4.00000

0

1.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(3\)	\( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	192.2.a.c		1
3.b	odd	2	1		576.2.a.h		1
4.b	odd	2	1		192.2.a.a		1
5.b	even	2	1		4800.2.a.f		1
5.c	odd	4	2		4800.2.f.bh		2
7.b	odd	2	1		9408.2.a.bj		1
8.b	even	2	1		96.2.a.a	✓	1
8.d	odd	2	1		96.2.a.b	yes	1
12.b	even	2	1		576.2.a.g		1
16.e	even	4	2		768.2.d.a		2
16.f	odd	4	2		768.2.d.h		2
20.d	odd	2	1		4800.2.a.co		1
20.e	even	4	2		4800.2.f.e		2
24.f	even	2	1		288.2.a.b		1
24.h	odd	2	1		288.2.a.c		1
28.d	even	2	1		9408.2.a.ct		1
40.e	odd	2	1		2400.2.a.q		1
40.f	even	2	1		2400.2.a.r		1
40.i	odd	4	2		2400.2.f.a		2
40.k	even	4	2		2400.2.f.r		2
48.i	odd	4	2		2304.2.d.c		2
48.k	even	4	2		2304.2.d.s		2
56.e	even	2	1		4704.2.a.e		1
56.h	odd	2	1		4704.2.a.t		1
72.j	odd	6	2		2592.2.i.q		2
72.l	even	6	2		2592.2.i.w		2
72.n	even	6	2		2592.2.i.b		2
72.p	odd	6	2		2592.2.i.h		2
120.i	odd	2	1		7200.2.a.e		1
120.m	even	2	1		7200.2.a.bx		1
120.q	odd	4	2		7200.2.f.f		2
120.w	even	4	2		7200.2.f.x		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
96.2.a.a	✓	1	8.b	even	2	1
96.2.a.b	yes	1	8.d	odd	2	1
192.2.a.a		1	4.b	odd	2	1
192.2.a.c		1	1.a	even	1	1	trivial
288.2.a.b		1	24.f	even	2	1
288.2.a.c		1	24.h	odd	2	1
576.2.a.g		1	12.b	even	2	1
576.2.a.h		1	3.b	odd	2	1
768.2.d.a		2	16.e	even	4	2
768.2.d.h		2	16.f	odd	4	2
2304.2.d.c		2	48.i	odd	4	2
2304.2.d.s		2	48.k	even	4	2
2400.2.a.q		1	40.e	odd	2	1
2400.2.a.r		1	40.f	even	2	1
2400.2.f.a		2	40.i	odd	4	2
2400.2.f.r		2	40.k	even	4	2
2592.2.i.b		2	72.n	even	6	2
2592.2.i.h		2	72.p	odd	6	2
2592.2.i.q		2	72.j	odd	6	2
2592.2.i.w		2	72.l	even	6	2
4704.2.a.e		1	56.e	even	2	1
4704.2.a.t		1	56.h	odd	2	1
4800.2.a.f		1	5.b	even	2	1
4800.2.a.co		1	20.d	odd	2	1
4800.2.f.e		2	20.e	even	4	2
4800.2.f.bh		2	5.c	odd	4	2
7200.2.a.e		1	120.i	odd	2	1
7200.2.a.bx		1	120.m	even	2	1
7200.2.f.f		2	120.q	odd	4	2
7200.2.f.x		2	120.w	even	4	2
9408.2.a.bj		1	7.b	odd	2	1
9408.2.a.ct		1	28.d	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(192))\):

\( T_{5} + 2 \)

\( T_{7} - 4 \)

\( T_{11} - 4 \)

Hecke characteristic polynomials

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