Newform orbit 4356.2.a.u

• Label: 4356.2.a.u
• Level: $4356$
• Weight: $2$
• Character orbit: 4356.a
• Self dual: yes
• Analytic conductor: $34.783$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4356 = 2^{2} \cdot 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4356.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(34.7828351205\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Defining polynomial:	\( x^{2} - x - 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 44)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{5})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + b * q^5 + (3*b - 1) * q^7 + (b - 4) * q^13 + (-b + 4) * q^17 + (-3*b + 1) * q^19 + (4*b - 4) * q^23 + (b - 4) * q^25 + (b + 7) * q^29 + (3*b - 4) * q^31 + (2*b + 3) * q^35 + (-3*b + 3) * q^37 + (b + 7) * q^41 + (b - 3) * q^47 + (3*b + 3) * q^49 + (5*b - 4) * q^53 + (-5*b + 7) * q^59 + (b - 4) * q^61 + (-3*b + 1) * q^65 + 8*b * q^67 + (-b + 8) * q^71 + (-5*b + 9) * q^73 + (-3*b + 12) * q^79 + (13*b - 8) * q^83 + (3*b - 1) * q^85 + (-4*b + 6) * q^89 + (-10*b + 7) * q^91 + (-2*b - 3) * q^95 - 9*b * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q + q^5 + q^7 - 7 * q^13 + 7 * q^17 - q^19 - 4 * q^23 - 7 * q^25 + 15 * q^29 - 5 * q^31 + 8 * q^35 + 3 * q^37 + 15 * q^41 - 5 * q^47 + 9 * q^49 - 3 * q^53 + 9 * q^59 - 7 * q^61 - q^65 + 8 * q^67 + 15 * q^71 + 13 * q^73 + 21 * q^79 - 3 * q^83 + q^85 + 8 * q^89 + 4 * q^91 - 8 * q^95 - 9 * 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

−0.618034
1.61803

0

0

0

−0.618034

0

−2.85410

0

0

0

1.2

0

0

0

1.61803

0

3.85410

0

0

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(3\)	\( -1 \)
\(11\)	\( -1 \)

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	4356.2.a.u		2
3.b	odd	2	1		484.2.a.c		2
11.b	odd	2	1		4356.2.a.t		2
11.d	odd	10	2		396.2.j.a		4
12.b	even	2	1		1936.2.a.z		2
24.f	even	2	1		7744.2.a.bo		2
24.h	odd	2	1		7744.2.a.db		2
33.d	even	2	1		484.2.a.b		2
33.f	even	10	2		44.2.e.a	✓	4
33.f	even	10	2		484.2.e.e		4
33.h	odd	10	2		484.2.e.c		4
33.h	odd	10	2		484.2.e.d		4
132.d	odd	2	1		1936.2.a.ba		2
132.n	odd	10	2		176.2.m.b		4
165.r	even	10	2		1100.2.n.a		4
165.u	odd	20	4		1100.2.cb.a		8
264.m	even	2	1		7744.2.a.da		2
264.p	odd	2	1		7744.2.a.bp		2
264.r	odd	10	2		704.2.m.d		4
264.u	even	10	2		704.2.m.e		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
44.2.e.a	✓	4	33.f	even	10	2
176.2.m.b		4	132.n	odd	10	2
396.2.j.a		4	11.d	odd	10	2
484.2.a.b		2	33.d	even	2	1
484.2.a.c		2	3.b	odd	2	1
484.2.e.c		4	33.h	odd	10	2
484.2.e.d		4	33.h	odd	10	2
484.2.e.e		4	33.f	even	10	2
704.2.m.d		4	264.r	odd	10	2
704.2.m.e		4	264.u	even	10	2
1100.2.n.a		4	165.r	even	10	2
1100.2.cb.a		8	165.u	odd	20	4
1936.2.a.z		2	12.b	even	2	1
1936.2.a.ba		2	132.d	odd	2	1
4356.2.a.t		2	11.b	odd	2	1
4356.2.a.u		2	1.a	even	1	1	trivial
7744.2.a.bo		2	24.f	even	2	1
7744.2.a.bp		2	264.p	odd	2	1
7744.2.a.da		2	264.m	even	2	1
7744.2.a.db		2	24.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4356))\):

\( T_{5}^{2} - T_{5} - 1 \)

\( T_{7}^{2} - T_{7} - 11 \)

Hecke characteristic polynomials

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