Newform orbit 676.2.a.b

• Label: 676.2.a.b
• Level: $676$
• Weight: $2$
• Character orbit: 676.a
• Self dual: yes
• Analytic conductor: $5.398$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(5.39788717664\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 52)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

q - 2 * q^3 + 3 * q^5 + 4 * q^7 + q^9 - 6 * q^15 + 3 * q^17 - 2 * q^19 - 8 * q^21 - 6 * q^23 + 4 * q^25 + 4 * q^27 + 9 * q^29 - 2 * q^31 + 12 * q^35 + 7 * q^37 - 3 * q^41 - 4 * q^43 + 3 * q^45 + 6 * q^47 + 9 * q^49 - 6 * q^51 + 9 * q^53 + 4 * q^57 + 5 * q^61 + 4 * q^63 - 2 * q^67 + 12 * q^69 + 6 * q^71 + q^73 - 8 * q^75 - 4 * q^79 - 11 * q^81 - 12 * q^83 + 9 * q^85 - 18 * q^87 - 6 * q^89 + 4 * q^93 - 6 * q^95 - 14 * q^97

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

−2.00000

0

3.00000

0

4.00000

0

1.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(13\)	\( +1 \)

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	676.2.a.b		1
3.b	odd	2	1		6084.2.a.c		1
4.b	odd	2	1		2704.2.a.m		1
13.b	even	2	1		676.2.a.a		1
13.c	even	3	2		676.2.e.d		2
13.d	odd	4	2		676.2.d.a		2
13.e	even	6	2		52.2.e.b	✓	2
13.f	odd	12	4		676.2.h.d		4
39.d	odd	2	1		6084.2.a.o		1
39.f	even	4	2		6084.2.b.k		2
39.h	odd	6	2		468.2.l.d		2
52.b	odd	2	1		2704.2.a.l		1
52.f	even	4	2		2704.2.f.i		2
52.i	odd	6	2		208.2.i.a		2
65.l	even	6	2		1300.2.i.b		2
65.r	odd	12	4		1300.2.bb.d		4
91.k	even	6	2		2548.2.i.g		2
91.l	odd	6	2		2548.2.i.b		2
91.p	odd	6	2		2548.2.l.g		2
91.t	odd	6	2		2548.2.k.a		2
91.u	even	6	2		2548.2.l.b		2
104.p	odd	6	2		832.2.i.i		2
104.s	even	6	2		832.2.i.c		2
156.r	even	6	2		1872.2.t.m		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
52.2.e.b	✓	2	13.e	even	6	2
208.2.i.a		2	52.i	odd	6	2
468.2.l.d		2	39.h	odd	6	2
676.2.a.a		1	13.b	even	2	1
676.2.a.b		1	1.a	even	1	1	trivial
676.2.d.a		2	13.d	odd	4	2
676.2.e.d		2	13.c	even	3	2
676.2.h.d		4	13.f	odd	12	4
832.2.i.c		2	104.s	even	6	2
832.2.i.i		2	104.p	odd	6	2
1300.2.i.b		2	65.l	even	6	2
1300.2.bb.d		4	65.r	odd	12	4
1872.2.t.m		2	156.r	even	6	2
2548.2.i.b		2	91.l	odd	6	2
2548.2.i.g		2	91.k	even	6	2
2548.2.k.a		2	91.t	odd	6	2
2548.2.l.b		2	91.u	even	6	2
2548.2.l.g		2	91.p	odd	6	2
2704.2.a.l		1	52.b	odd	2	1
2704.2.a.m		1	4.b	odd	2	1
2704.2.f.i		2	52.f	even	4	2
6084.2.a.c		1	3.b	odd	2	1
6084.2.a.o		1	39.d	odd	2	1
6084.2.b.k		2	39.f	even	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(676))\):

\( T_{3} + 2 \)

\( T_{5} - 3 \)

Hecke characteristic polynomials

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