Newform orbit 5440.2.a.bi

• Label: 5440.2.a.bi
• Level: $5440$
• Weight: $2$
• Character orbit: 5440.a
• Self dual: yes
• Analytic conductor: $43.439$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5440 = 2^{6} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5440.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(43.4386186996\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{2}) \)
Defining polynomial:	\( x^{2} - 2 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 680)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(f(q)\)	\(=\)	q + b * q^3 + q^5 + b * q^7 - q^9 + (-3*b + 2) * q^11 + (-2*b + 4) * q^13 + b * q^15 - q^17 + (2*b + 4) * q^19 + 2 * q^21 + (-b + 4) * q^23 + q^25 - 4*b * q^27 + (6*b + 2) * q^29 + (-3*b + 2) * q^31 + (2*b - 6) * q^33 + b * q^35 + (6*b + 2) * q^37 + (4*b - 4) * q^39 + (-2*b - 6) * q^41 + (-2*b + 2) * q^43 - q^45 + (-4*b + 6) * q^47 - 5 * q^49 - b * q^51 + (-4*b + 2) * q^53 + (-3*b + 2) * q^55 + (4*b + 4) * q^57 + 2*b * q^59 + (-4*b + 6) * q^61 - b * q^63 + (-2*b + 4) * q^65 + (4*b - 2) * q^67 + (4*b - 2) * q^69 + (7*b + 6) * q^71 + (2*b - 10) * q^73 + b * q^75 + (2*b - 6) * q^77 + (-5*b - 6) * q^79 - 5 * q^81 + (6*b - 2) * q^83 - q^85 + (2*b + 12) * q^87 + (8*b + 4) * q^89 + (4*b - 4) * q^91 + (2*b - 6) * q^93 + (2*b + 4) * q^95 + (4*b - 2) * q^97 + (3*b - 2) * q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q + 2 * q^5 - 2 * q^9 + 4 * q^11 + 8 * q^13 - 2 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 2 * q^25 + 4 * q^29 + 4 * q^31 - 12 * q^33 + 4 * q^37 - 8 * q^39 - 12 * q^41 + 4 * q^43 - 2 * q^45 + 12 * q^47 - 10 * q^49 + 4 * q^53 + 4 * q^55 + 8 * q^57 + 12 * q^61 + 8 * q^65 - 4 * q^67 - 4 * q^69 + 12 * q^71 - 20 * q^73 - 12 * q^77 - 12 * q^79 - 10 * q^81 - 4 * q^83 - 2 * q^85 + 24 * q^87 + 8 * q^89 - 8 * q^91 - 12 * q^93 + 8 * q^95 - 4 * q^97 - 4 * q^99

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

−1.41421
1.41421

0

−1.41421

0

1.00000

0

−1.41421

0

−1.00000

0

1.2

0

1.41421

0

1.00000

0

1.41421

0

−1.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(5\)	\( -1 \)
\(17\)	\( +1 \)

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	5440.2.a.bi		2
4.b	odd	2	1		5440.2.a.bg		2
8.b	even	2	1		680.2.a.e	✓	2
8.d	odd	2	1		1360.2.a.l		2
24.h	odd	2	1		6120.2.a.bl		2
40.e	odd	2	1		6800.2.a.bf		2
40.f	even	2	1		3400.2.a.h		2
40.i	odd	4	2		3400.2.e.h		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
680.2.a.e	✓	2	8.b	even	2	1
1360.2.a.l		2	8.d	odd	2	1
3400.2.a.h		2	40.f	even	2	1
3400.2.e.h		4	40.i	odd	4	2
5440.2.a.bg		2	4.b	odd	2	1
5440.2.a.bi		2	1.a	even	1	1	trivial
6120.2.a.bl		2	24.h	odd	2	1
6800.2.a.bf		2	40.e	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5440))\):

\( T_{3}^{2} - 2 \)

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

\( T_{11}^{2} - 4T_{11} - 14 \)

\( T_{13}^{2} - 8T_{13} + 8 \)

\( T_{19}^{2} - 8T_{19} + 8 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} - 2 \)
$5$	\( (T - 1)^{2} \)
$7$	\( T^{2} - 2 \)
$11$	\( T^{2} - 4T - 14 \)