Newform orbit 4900.2.a.n

• Label: 4900.2.a.n
• Level: $4900$
• Weight: $2$
• Character orbit: 4900.a
• Self dual: yes
• Analytic conductor: $39.127$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4900.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(39.1266969904\)
Analytic rank:	\(1\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 28)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

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

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

0

0

0

0

−2.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(5\)	\(1\)
\(7\)	\(-1\)

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	4900.2.a.n		1
5.b	even	2	1		196.2.a.a		1
5.c	odd	4	2		4900.2.e.h		2
7.b	odd	2	1		4900.2.a.g		1
7.d	odd	6	2		700.2.i.c		2
15.d	odd	2	1		1764.2.a.j		1
20.d	odd	2	1		784.2.a.g		1
35.c	odd	2	1		196.2.a.b		1
35.f	even	4	2		4900.2.e.i		2
35.i	odd	6	2		28.2.e.a	✓	2
35.j	even	6	2		196.2.e.a		2
35.k	even	12	4		700.2.r.b		4
40.e	odd	2	1		3136.2.a.k		1
40.f	even	2	1		3136.2.a.v		1
60.h	even	2	1		7056.2.a.bw		1
105.g	even	2	1		1764.2.a.a		1
105.o	odd	6	2		1764.2.k.b		2
105.p	even	6	2		252.2.k.c		2
140.c	even	2	1		784.2.a.d		1
140.p	odd	6	2		784.2.i.d		2
140.s	even	6	2		112.2.i.b		2
280.c	odd	2	1		3136.2.a.h		1
280.n	even	2	1		3136.2.a.s		1
280.ba	even	6	2		448.2.i.c		2
280.bk	odd	6	2		448.2.i.e		2
315.q	odd	6	2		2268.2.i.a		2
315.u	even	6	2		2268.2.l.a		2
315.bn	odd	6	2		2268.2.l.h		2
315.bq	even	6	2		2268.2.i.h		2
420.o	odd	2	1		7056.2.a.f		1
420.be	odd	6	2		1008.2.s.p		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
28.2.e.a	✓	2	35.i	odd	6	2
112.2.i.b		2	140.s	even	6	2
196.2.a.a		1	5.b	even	2	1
196.2.a.b		1	35.c	odd	2	1
196.2.e.a		2	35.j	even	6	2
252.2.k.c		2	105.p	even	6	2
448.2.i.c		2	280.ba	even	6	2
448.2.i.e		2	280.bk	odd	6	2
700.2.i.c		2	7.d	odd	6	2
700.2.r.b		4	35.k	even	12	4
784.2.a.d		1	140.c	even	2	1
784.2.a.g		1	20.d	odd	2	1
784.2.i.d		2	140.p	odd	6	2
1008.2.s.p		2	420.be	odd	6	2
1764.2.a.a		1	105.g	even	2	1
1764.2.a.j		1	15.d	odd	2	1
1764.2.k.b		2	105.o	odd	6	2
2268.2.i.a		2	315.q	odd	6	2
2268.2.i.h		2	315.bq	even	6	2
2268.2.l.a		2	315.u	even	6	2
2268.2.l.h		2	315.bn	odd	6	2
3136.2.a.h		1	280.c	odd	2	1
3136.2.a.k		1	40.e	odd	2	1
3136.2.a.s		1	280.n	even	2	1
3136.2.a.v		1	40.f	even	2	1
4900.2.a.g		1	7.b	odd	2	1
4900.2.a.n		1	1.a	even	1	1	trivial
4900.2.e.h		2	5.c	odd	4	2
4900.2.e.i		2	35.f	even	4	2
7056.2.a.f		1	420.o	odd	2	1
7056.2.a.bw		1	60.h	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4900))\):

\( T_{3} - 1 \)

\( T_{11} + 3 \)

\( T_{13} - 2 \)

\( T_{19} - 1 \)

\( T_{23} + 3 \)

Hecke characteristic polynomials

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