# Properties

 Label 5796.2.a.l Level $5796$ Weight $2$ Character orbit 5796.a Self dual yes Analytic conductor $46.281$ Analytic rank $0$ 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: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{5})$$ Defining polynomial: $$x^{2} - x - 1$$ x^2 - x - 1 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 $$\beta = \frac{1}{2}(1 + \sqrt{5})$$. 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 $$q + \beta q^{5} - q^{7} + 3 q^{11} + (\beta - 1) q^{13} + ( - 6 \beta + 3) q^{17} + ( - 2 \beta - 1) q^{19} + q^{23} + (\beta - 4) q^{25} + ( - 2 \beta + 5) q^{29} - 3 q^{31} - \beta q^{35} + (4 \beta + 3) q^{37} + (8 \beta - 1) q^{41} + ( - 5 \beta - 1) q^{43} + (2 \beta + 6) q^{47} + q^{49} + (7 \beta - 2) q^{53} + 3 \beta q^{55} + (\beta + 8) q^{59} + (3 \beta + 1) q^{61} + q^{65} + (9 \beta - 8) q^{67} + (\beta + 3) q^{71} + ( - 2 \beta + 5) q^{73} - 3 q^{77} + ( - 6 \beta + 3) q^{79} + (4 \beta + 1) q^{83} + ( - 3 \beta - 6) q^{85} + (11 \beta - 1) q^{89} + ( - \beta + 1) q^{91} + ( - 3 \beta - 2) q^{95} + ( - 12 \beta + 7) q^{97} +O(q^{100})$$ q + b * q^5 - q^7 + 3 * q^11 + (b - 1) * q^13 + (-6*b + 3) * q^17 + (-2*b - 1) * q^19 + q^23 + (b - 4) * q^25 + (-2*b + 5) * q^29 - 3 * q^31 - b * q^35 + (4*b + 3) * q^37 + (8*b - 1) * q^41 + (-5*b - 1) * q^43 + (2*b + 6) * q^47 + q^49 + (7*b - 2) * q^53 + 3*b * q^55 + (b + 8) * q^59 + (3*b + 1) * q^61 + q^65 + (9*b - 8) * q^67 + (b + 3) * q^71 + (-2*b + 5) * q^73 - 3 * q^77 + (-6*b + 3) * q^79 + (4*b + 1) * q^83 + (-3*b - 6) * q^85 + (11*b - 1) * q^89 + (-b + 1) * q^91 + (-3*b - 2) * q^95 + (-12*b + 7) * q^97 $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{5} - 2 q^{7}+O(q^{10})$$ 2 * q + q^5 - 2 * q^7 $$2 q + q^{5} - 2 q^{7} + 6 q^{11} - q^{13} - 4 q^{19} + 2 q^{23} - 7 q^{25} + 8 q^{29} - 6 q^{31} - q^{35} + 10 q^{37} + 6 q^{41} - 7 q^{43} + 14 q^{47} + 2 q^{49} + 3 q^{53} + 3 q^{55} + 17 q^{59} + 5 q^{61} + 2 q^{65} - 7 q^{67} + 7 q^{71} + 8 q^{73} - 6 q^{77} + 6 q^{83} - 15 q^{85} + 9 q^{89} + q^{91} - 7 q^{95} + 2 q^{97}+O(q^{100})$$ 2 * q + q^5 - 2 * q^7 + 6 * q^11 - q^13 - 4 * q^19 + 2 * q^23 - 7 * q^25 + 8 * q^29 - 6 * q^31 - q^35 + 10 * q^37 + 6 * q^41 - 7 * q^43 + 14 * q^47 + 2 * q^49 + 3 * q^53 + 3 * q^55 + 17 * q^59 + 5 * q^61 + 2 * q^65 - 7 * q^67 + 7 * q^71 + 8 * q^73 - 6 * q^77 + 6 * q^83 - 15 * q^85 + 9 * q^89 + q^91 - 7 * 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
 −0.618034 1.61803
0 0 0 −0.618034 0 −1.00000 0 0 0
1.2 0 0 0 1.61803 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.l 2
3.b odd 2 1 1932.2.a.g 2
12.b even 2 1 7728.2.a.ba 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1932.2.a.g 2 3.b odd 2 1
5796.2.a.l 2 1.a even 1 1 trivial
7728.2.a.ba 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 $$S_{2}^{\mathrm{new}}(\Gamma_0(5796))$$:

 $$T_{5}^{2} - T_{5} - 1$$ T5^2 - T5 - 1 $$T_{11} - 3$$ T11 - 3

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{2}$$
$3$ $$T^{2}$$
$5$ $$T^{2} - T - 1$$
$7$ $$(T + 1)^{2}$$
$11$ $$(T - 3)^{2}$$
$13$ $$T^{2} + T - 1$$
$17$ $$T^{2} - 45$$
$19$ $$T^{2} + 4T - 1$$
$23$ $$(T - 1)^{2}$$
$29$ $$T^{2} - 8T + 11$$
$31$ $$(T + 3)^{2}$$
$37$ $$T^{2} - 10T + 5$$
$41$ $$T^{2} - 6T - 71$$
$43$ $$T^{2} + 7T - 19$$
$47$ $$T^{2} - 14T + 44$$
$53$ $$T^{2} - 3T - 59$$
$59$ $$T^{2} - 17T + 71$$
$61$ $$T^{2} - 5T - 5$$
$67$ $$T^{2} + 7T - 89$$
$71$ $$T^{2} - 7T + 11$$
$73$ $$T^{2} - 8T + 11$$
$79$ $$T^{2} - 45$$
$83$ $$T^{2} - 6T - 11$$
$89$ $$T^{2} - 9T - 131$$
$97$ $$T^{2} - 2T - 179$$