# Properties

 Label 5184.2.a.v Level $5184$ Weight $2$ Character orbit 5184.a Self dual yes Analytic conductor $41.394$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

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## Newspace parameters

 Level: $$N$$ $$=$$ $$5184 = 2^{6} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5184.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$41.3944484078$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 648) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{5}+O(q^{10})$$ q + q^5 $$q + q^{5} + 4 q^{11} + 5 q^{13} - 5 q^{17} - 8 q^{19} - 4 q^{23} - 4 q^{25} - 3 q^{29} - 4 q^{31} - 3 q^{37} - 6 q^{41} - 4 q^{43} - 12 q^{47} - 7 q^{49} + 10 q^{53} + 4 q^{55} - 8 q^{59} + 5 q^{61} + 5 q^{65} - 8 q^{67} + 16 q^{71} - 5 q^{73} + 4 q^{79} - 4 q^{83} - 5 q^{85} + 3 q^{89} - 8 q^{95} + 2 q^{97}+O(q^{100})$$ q + q^5 + 4 * q^11 + 5 * q^13 - 5 * q^17 - 8 * q^19 - 4 * q^23 - 4 * q^25 - 3 * q^29 - 4 * q^31 - 3 * q^37 - 6 * q^41 - 4 * q^43 - 12 * q^47 - 7 * q^49 + 10 * q^53 + 4 * q^55 - 8 * q^59 + 5 * q^61 + 5 * q^65 - 8 * q^67 + 16 * q^71 - 5 * q^73 + 4 * q^79 - 4 * q^83 - 5 * q^85 + 3 * q^89 - 8 * q^95 + 2 * 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 0 0 1.00000 0 0 0 0 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$3$$ $$1$$

## 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 5184.2.a.v 1
3.b odd 2 1 5184.2.a.k 1
4.b odd 2 1 5184.2.a.u 1
8.b even 2 1 648.2.a.b 1
8.d odd 2 1 1296.2.a.d 1
12.b even 2 1 5184.2.a.l 1
24.f even 2 1 1296.2.a.h 1
24.h odd 2 1 648.2.a.d yes 1
72.j odd 6 2 648.2.i.d 2
72.l even 6 2 1296.2.i.f 2
72.n even 6 2 648.2.i.f 2
72.p odd 6 2 1296.2.i.k 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
648.2.a.b 1 8.b even 2 1
648.2.a.d yes 1 24.h odd 2 1
648.2.i.d 2 72.j odd 6 2
648.2.i.f 2 72.n even 6 2
1296.2.a.d 1 8.d odd 2 1
1296.2.a.h 1 24.f even 2 1
1296.2.i.f 2 72.l even 6 2
1296.2.i.k 2 72.p odd 6 2
5184.2.a.k 1 3.b odd 2 1
5184.2.a.l 1 12.b even 2 1
5184.2.a.u 1 4.b odd 2 1
5184.2.a.v 1 1.a even 1 1 trivial

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5184))$$:

 $$T_{5} - 1$$ T5 - 1 $$T_{7}$$ T7 $$T_{11} - 4$$ T11 - 4

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T$$
$5$ $$T - 1$$
$7$ $$T$$
$11$ $$T - 4$$
$13$ $$T - 5$$
$17$ $$T + 5$$
$19$ $$T + 8$$
$23$ $$T + 4$$
$29$ $$T + 3$$
$31$ $$T + 4$$
$37$ $$T + 3$$
$41$ $$T + 6$$
$43$ $$T + 4$$
$47$ $$T + 12$$
$53$ $$T - 10$$
$59$ $$T + 8$$
$61$ $$T - 5$$
$67$ $$T + 8$$
$71$ $$T - 16$$
$73$ $$T + 5$$
$79$ $$T - 4$$
$83$ $$T + 4$$
$89$ $$T - 3$$
$97$ $$T - 2$$
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