Newform orbit 98.10.a.c

• Label: 98.10.a.c
• Level: $98$
• Weight: $10$
• Character orbit: 98.a
• Self dual: yes
• Analytic conductor: $50.474$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(50.4735119441\)
Analytic rank:	\(1\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q + 16 q^{2} + 156 q^{3} + 256 q^{4} - 870 q^{5} + 2496 q^{6} + 4096 q^{8} + 4653 q^{9}+O(q^{10}) \)

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

16.0000

156.000

256.000

−870.000

2496.00

0

4096.00

4653.00

−13920.0

Atkin-Lehner signs

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

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	98.10.a.c		1
7.b	odd	2	1		2.10.a.a	✓	1
7.c	even	3	2		98.10.c.b		2
7.d	odd	6	2		98.10.c.c		2
21.c	even	2	1		18.10.a.a		1
28.d	even	2	1		16.10.a.d		1
35.c	odd	2	1		50.10.a.c		1
35.f	even	4	2		50.10.b.a		2
56.e	even	2	1		64.10.a.b		1
56.h	odd	2	1		64.10.a.h		1
63.l	odd	6	2		162.10.c.b		2
63.o	even	6	2		162.10.c.i		2
77.b	even	2	1		242.10.a.a		1
84.h	odd	2	1		144.10.a.d		1
91.b	odd	2	1		338.10.a.a		1
112.j	even	4	2		256.10.b.e		2
112.l	odd	4	2		256.10.b.g		2
140.c	even	2	1		400.10.a.b		1
140.j	odd	4	2		400.10.c.d		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2.10.a.a	✓	1	7.b	odd	2	1
16.10.a.d		1	28.d	even	2	1
18.10.a.a		1	21.c	even	2	1
50.10.a.c		1	35.c	odd	2	1
50.10.b.a		2	35.f	even	4	2
64.10.a.b		1	56.e	even	2	1
64.10.a.h		1	56.h	odd	2	1
98.10.a.c		1	1.a	even	1	1	trivial
98.10.c.b		2	7.c	even	3	2
98.10.c.c		2	7.d	odd	6	2
144.10.a.d		1	84.h	odd	2	1
162.10.c.b		2	63.l	odd	6	2
162.10.c.i		2	63.o	even	6	2
242.10.a.a		1	77.b	even	2	1
256.10.b.e		2	112.j	even	4	2
256.10.b.g		2	112.l	odd	4	2
338.10.a.a		1	91.b	odd	2	1
400.10.a.b		1	140.c	even	2	1
400.10.c.d		2	140.j	odd	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 156 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(98))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 16 \)
$3$	\( T - 156 \)
$5$	\( T + 870 \)
$7$	\( T \)
$11$	\( T + 56148 \)