Newform orbit 5440.2.a.bd

• Label: 5440.2.a.bd
• Level: $5440$
• Weight: $2$
• Character orbit: 5440.a
• Self dual: yes
• Analytic conductor: $43.439$
• Analytic rank: $1$
• 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:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{17}) \)
Defining polynomial:	\( x^{2} - x - 4 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 170)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{17})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q - b * q^3 - q^5 - 2*b * q^7 + (b + 1) * q^9 - 4 * q^11 + (-b - 2) * q^13 + b * q^15 + q^17 - b * q^19 + (2*b + 8) * q^21 + 2*b * q^23 + q^25 + (b - 4) * q^27 + (3*b - 2) * q^29 + (b + 4) * q^31 + 4*b * q^33 + 2*b * q^35 + (2*b + 2) * q^37 + (3*b + 4) * q^39 + (4*b - 6) * q^41 + (-2*b + 4) * q^43 + (-b - 1) * q^45 + (-b - 4) * q^47 + (4*b + 9) * q^49 - b * q^51 + (b - 2) * q^53 + 4 * q^55 + (b + 4) * q^57 + (3*b - 8) * q^59 + (b - 10) * q^61 + (-4*b - 8) * q^63 + (b + 2) * q^65 + (-2*b - 4) * q^67 + (-2*b - 8) * q^69 + (-3*b + 12) * q^71 + (-5*b + 6) * q^73 - b * q^75 + 8*b * q^77 - 7 * q^81 + (-4*b + 4) * q^83 - q^85 + (-b - 12) * q^87 + (-3*b - 2) * q^89 + (6*b + 8) * q^91 + (-5*b - 4) * q^93 + b * q^95 + (-3*b + 6) * q^97 + (-4*b - 4) * q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - q^3 - 2 * q^5 - 2 * q^7 + 3 * q^9 - 8 * q^11 - 5 * q^13 + q^15 + 2 * q^17 - q^19 + 18 * q^21 + 2 * q^23 + 2 * q^25 - 7 * q^27 - q^29 + 9 * q^31 + 4 * q^33 + 2 * q^35 + 6 * q^37 + 11 * q^39 - 8 * q^41 + 6 * q^43 - 3 * q^45 - 9 * q^47 + 22 * q^49 - q^51 - 3 * q^53 + 8 * q^55 + 9 * q^57 - 13 * q^59 - 19 * q^61 - 20 * q^63 + 5 * q^65 - 10 * q^67 - 18 * q^69 + 21 * q^71 + 7 * q^73 - q^75 + 8 * q^77 - 14 * q^81 + 4 * q^83 - 2 * q^85 - 25 * q^87 - 7 * q^89 + 22 * q^91 - 13 * q^93 + q^95 + 9 * q^97 - 12 * 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

2.56155
−1.56155

0

−2.56155

0

−1.00000

0

−5.12311

0

3.56155

0

1.2

0

1.56155

0

−1.00000

0

3.12311

0

−0.561553

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.bd		2
4.b	odd	2	1		5440.2.a.bj		2
8.b	even	2	1		1360.2.a.m		2
8.d	odd	2	1		170.2.a.f	✓	2
24.f	even	2	1		1530.2.a.r		2
40.e	odd	2	1		850.2.a.n		2
40.f	even	2	1		6800.2.a.be		2
40.k	even	4	2		850.2.c.i		4
56.e	even	2	1		8330.2.a.bq		2
120.m	even	2	1		7650.2.a.de		2
136.e	odd	2	1		2890.2.a.u		2
136.j	odd	4	2		2890.2.b.i		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
170.2.a.f	✓	2	8.d	odd	2	1
850.2.a.n		2	40.e	odd	2	1
850.2.c.i		4	40.k	even	4	2
1360.2.a.m		2	8.b	even	2	1
1530.2.a.r		2	24.f	even	2	1
2890.2.a.u		2	136.e	odd	2	1
2890.2.b.i		4	136.j	odd	4	2
5440.2.a.bd		2	1.a	even	1	1	trivial
5440.2.a.bj		2	4.b	odd	2	1
6800.2.a.be		2	40.f	even	2	1
7650.2.a.de		2	120.m	even	2	1
8330.2.a.bq		2	56.e	even	2	1

Hecke kernels

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

\( T_{3}^{2} + T_{3} - 4 \)

\( T_{7}^{2} + 2T_{7} - 16 \)

\( T_{11} + 4 \)

\( T_{13}^{2} + 5T_{13} + 2 \)

\( T_{19}^{2} + T_{19} - 4 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} + T - 4 \)
$5$	\( (T + 1)^{2} \)
$7$	\( T^{2} + 2T - 16 \)
$11$	\( (T + 4)^{2} \)