# Properties

 Label 5796.2.a.k Level $5796$ Weight $2$ Character orbit 5796.a Self dual yes Analytic conductor $46.281$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5796.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$46.2812930115$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{13})$$ Defining polynomial: $$x^{2} - x - 3$$ x^2 - x - 3 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1932) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of $$\beta = \frac{1}{2}(1 + \sqrt{13})$$. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q - \beta q^{5} + q^{7} +O(q^{10})$$ q - b * q^5 + q^7 $$q - \beta q^{5} + q^{7} + (2 \beta - 1) q^{11} + (\beta - 3) q^{13} + 3 q^{17} + ( - 2 \beta - 3) q^{19} + q^{23} + (\beta - 2) q^{25} - q^{29} + q^{31} - \beta q^{35} + ( - 4 \beta + 1) q^{37} + (2 \beta + 1) q^{41} + ( - 3 \beta - 1) q^{43} + (2 \beta + 6) q^{47} + q^{49} + ( - 3 \beta - 6) q^{53} + ( - \beta - 6) q^{55} + ( - 3 \beta - 4) q^{59} + (5 \beta - 3) q^{61} + (2 \beta - 3) q^{65} + (7 \beta - 6) q^{67} + (3 \beta + 5) q^{71} + (6 \beta - 3) q^{73} + (2 \beta - 1) q^{77} + (2 \beta - 11) q^{79} + ( - 2 \beta + 5) q^{83} - 3 \beta q^{85} + ( - \beta - 1) q^{89} + (\beta - 3) q^{91} + (5 \beta + 6) q^{95} - 11 q^{97} +O(q^{100})$$ q - b * q^5 + q^7 + (2*b - 1) * q^11 + (b - 3) * q^13 + 3 * q^17 + (-2*b - 3) * q^19 + q^23 + (b - 2) * q^25 - q^29 + q^31 - b * q^35 + (-4*b + 1) * q^37 + (2*b + 1) * q^41 + (-3*b - 1) * q^43 + (2*b + 6) * q^47 + q^49 + (-3*b - 6) * q^53 + (-b - 6) * q^55 + (-3*b - 4) * q^59 + (5*b - 3) * q^61 + (2*b - 3) * q^65 + (7*b - 6) * q^67 + (3*b + 5) * q^71 + (6*b - 3) * q^73 + (2*b - 1) * q^77 + (2*b - 11) * q^79 + (-2*b + 5) * q^83 - 3*b * q^85 + (-b - 1) * q^89 + (b - 3) * q^91 + (5*b + 6) * q^95 - 11 * q^97 $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{5} + 2 q^{7}+O(q^{10})$$ 2 * q - q^5 + 2 * q^7 $$2 q - q^{5} + 2 q^{7} - 5 q^{13} + 6 q^{17} - 8 q^{19} + 2 q^{23} - 3 q^{25} - 2 q^{29} + 2 q^{31} - q^{35} - 2 q^{37} + 4 q^{41} - 5 q^{43} + 14 q^{47} + 2 q^{49} - 15 q^{53} - 13 q^{55} - 11 q^{59} - q^{61} - 4 q^{65} - 5 q^{67} + 13 q^{71} - 20 q^{79} + 8 q^{83} - 3 q^{85} - 3 q^{89} - 5 q^{91} + 17 q^{95} - 22 q^{97}+O(q^{100})$$ 2 * q - q^5 + 2 * q^7 - 5 * q^13 + 6 * q^17 - 8 * q^19 + 2 * q^23 - 3 * q^25 - 2 * q^29 + 2 * q^31 - q^35 - 2 * q^37 + 4 * q^41 - 5 * q^43 + 14 * q^47 + 2 * q^49 - 15 * q^53 - 13 * q^55 - 11 * q^59 - q^61 - 4 * q^65 - 5 * q^67 + 13 * q^71 - 20 * q^79 + 8 * q^83 - 3 * q^85 - 3 * q^89 - 5 * q^91 + 17 * q^95 - 22 * 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
 2.30278 −1.30278
0 0 0 −2.30278 0 1.00000 0 0 0
1.2 0 0 0 1.30278 0 1.00000 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
$$2$$ $$-1$$
$$3$$ $$-1$$
$$7$$ $$-1$$
$$23$$ $$-1$$

## 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 5796.2.a.k 2
3.b odd 2 1 1932.2.a.e 2
12.b even 2 1 7728.2.a.bk 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1932.2.a.e 2 3.b odd 2 1
5796.2.a.k 2 1.a even 1 1 trivial
7728.2.a.bk 2 12.b even 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5796))$$:

 $$T_{5}^{2} + T_{5} - 3$$ T5^2 + T5 - 3 $$T_{11}^{2} - 13$$ T11^2 - 13

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{2}$$
$3$ $$T^{2}$$
$5$ $$T^{2} + T - 3$$
$7$ $$(T - 1)^{2}$$
$11$ $$T^{2} - 13$$
$13$ $$T^{2} + 5T + 3$$
$17$ $$(T - 3)^{2}$$
$19$ $$T^{2} + 8T + 3$$
$23$ $$(T - 1)^{2}$$
$29$ $$(T + 1)^{2}$$
$31$ $$(T - 1)^{2}$$
$37$ $$T^{2} + 2T - 51$$
$41$ $$T^{2} - 4T - 9$$
$43$ $$T^{2} + 5T - 23$$
$47$ $$T^{2} - 14T + 36$$
$53$ $$T^{2} + 15T + 27$$
$59$ $$T^{2} + 11T + 1$$
$61$ $$T^{2} + T - 81$$
$67$ $$T^{2} + 5T - 153$$
$71$ $$T^{2} - 13T + 13$$
$73$ $$T^{2} - 117$$
$79$ $$T^{2} + 20T + 87$$
$83$ $$T^{2} - 8T + 3$$
$89$ $$T^{2} + 3T - 1$$
$97$ $$(T + 11)^{2}$$