Properties

 Label 2832.2.a.o Level $2832$ Weight $2$ Character orbit 2832.a Self dual yes Analytic conductor $22.614$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$2832 = 2^{4} \cdot 3 \cdot 59$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2832.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$22.6136338524$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{5})$$ Defining polynomial: $$x^{2} - x - 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 177) 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.

 $$f(q)$$ $$=$$ $$q + q^{3} + ( 1 - 2 \beta ) q^{5} + ( 4 - \beta ) q^{7} + q^{9} +O(q^{10})$$ $$q + q^{3} + ( 1 - 2 \beta ) q^{5} + ( 4 - \beta ) q^{7} + q^{9} + ( 1 - 2 \beta ) q^{11} + ( -3 - 2 \beta ) q^{13} + ( 1 - 2 \beta ) q^{15} + ( -3 + 3 \beta ) q^{17} + ( 5 - 5 \beta ) q^{19} + ( 4 - \beta ) q^{21} + ( 3 + \beta ) q^{23} + q^{27} + ( 8 - \beta ) q^{29} + ( -4 + 9 \beta ) q^{31} + ( 1 - 2 \beta ) q^{33} + ( 6 - 7 \beta ) q^{35} + ( -5 + 3 \beta ) q^{37} + ( -3 - 2 \beta ) q^{39} + 5 \beta q^{41} + ( -1 + 6 \beta ) q^{43} + ( 1 - 2 \beta ) q^{45} + ( 6 + 3 \beta ) q^{47} + ( 10 - 7 \beta ) q^{49} + ( -3 + 3 \beta ) q^{51} + ( 3 + 2 \beta ) q^{53} + 5 q^{55} + ( 5 - 5 \beta ) q^{57} + q^{59} + ( -8 + 3 \beta ) q^{61} + ( 4 - \beta ) q^{63} + ( 1 + 8 \beta ) q^{65} + ( -1 - 6 \beta ) q^{67} + ( 3 + \beta ) q^{69} + ( -5 + 8 \beta ) q^{71} + ( -4 + 3 \beta ) q^{73} + ( 6 - 7 \beta ) q^{77} + 3 q^{79} + q^{81} + \beta q^{83} + ( -9 + 3 \beta ) q^{85} + ( 8 - \beta ) q^{87} + ( 4 - 11 \beta ) q^{89} + ( -10 - 3 \beta ) q^{91} + ( -4 + 9 \beta ) q^{93} + ( 15 - 5 \beta ) q^{95} + 3 q^{97} + ( 1 - 2 \beta ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{3} + 7q^{7} + 2q^{9} + O(q^{10})$$ $$2q + 2q^{3} + 7q^{7} + 2q^{9} - 8q^{13} - 3q^{17} + 5q^{19} + 7q^{21} + 7q^{23} + 2q^{27} + 15q^{29} + q^{31} + 5q^{35} - 7q^{37} - 8q^{39} + 5q^{41} + 4q^{43} + 15q^{47} + 13q^{49} - 3q^{51} + 8q^{53} + 10q^{55} + 5q^{57} + 2q^{59} - 13q^{61} + 7q^{63} + 10q^{65} - 8q^{67} + 7q^{69} - 2q^{71} - 5q^{73} + 5q^{77} + 6q^{79} + 2q^{81} + q^{83} - 15q^{85} + 15q^{87} - 3q^{89} - 23q^{91} + q^{93} + 25q^{95} + 6q^{97} + O(q^{100})$$

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
 1.61803 −0.618034
0 1.00000 0 −2.23607 0 2.38197 0 1.00000 0
1.2 0 1.00000 0 2.23607 0 4.61803 0 1.00000 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
$$2$$ $$-1$$
$$3$$ $$-1$$
$$59$$ $$-1$$

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 2832.2.a.o 2
3.b odd 2 1 8496.2.a.bb 2
4.b odd 2 1 177.2.a.b 2
12.b even 2 1 531.2.a.b 2
20.d odd 2 1 4425.2.a.t 2
28.d even 2 1 8673.2.a.k 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
177.2.a.b 2 4.b odd 2 1
531.2.a.b 2 12.b even 2 1
2832.2.a.o 2 1.a even 1 1 trivial
4425.2.a.t 2 20.d odd 2 1
8496.2.a.bb 2 3.b odd 2 1
8673.2.a.k 2 28.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2832))$$:

 $$T_{5}^{2} - 5$$ $$T_{7}^{2} - 7 T_{7} + 11$$ $$T_{11}^{2} - 5$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{2}$$
$3$ $$( -1 + T )^{2}$$
$5$ $$-5 + T^{2}$$
$7$ $$11 - 7 T + T^{2}$$
$11$ $$-5 + T^{2}$$
$13$ $$11 + 8 T + T^{2}$$
$17$ $$-9 + 3 T + T^{2}$$
$19$ $$-25 - 5 T + T^{2}$$
$23$ $$11 - 7 T + T^{2}$$
$29$ $$55 - 15 T + T^{2}$$
$31$ $$-101 - T + T^{2}$$
$37$ $$1 + 7 T + T^{2}$$
$41$ $$-25 - 5 T + T^{2}$$
$43$ $$-41 - 4 T + T^{2}$$
$47$ $$45 - 15 T + T^{2}$$
$53$ $$11 - 8 T + T^{2}$$
$59$ $$( -1 + T )^{2}$$
$61$ $$31 + 13 T + T^{2}$$
$67$ $$-29 + 8 T + T^{2}$$
$71$ $$-79 + 2 T + T^{2}$$
$73$ $$-5 + 5 T + T^{2}$$
$79$ $$( -3 + T )^{2}$$
$83$ $$-1 - T + T^{2}$$
$89$ $$-149 + 3 T + T^{2}$$
$97$ $$( -3 + T )^{2}$$