# Properties

 Label 2736.2.a.v Level $2736$ Weight $2$ Character orbit 2736.a Self dual yes Analytic conductor $21.847$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2736.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$21.8470699930$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 57) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + 3q^{5} + 5q^{7} + O(q^{10})$$ $$q + 3q^{5} + 5q^{7} + q^{11} + 2q^{13} + q^{17} + q^{19} - 4q^{23} + 4q^{25} + 2q^{29} + 6q^{31} + 15q^{35} + q^{43} - 9q^{47} + 18q^{49} - 10q^{53} + 3q^{55} - 8q^{59} - q^{61} + 6q^{65} - 8q^{67} - 12q^{71} - 11q^{73} + 5q^{77} - 16q^{79} + 12q^{83} + 3q^{85} + 6q^{89} + 10q^{91} + 3q^{95} - 10q^{97} + O(q^{100})$$

## 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
 0
0 0 0 3.00000 0 5.00000 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
$$2$$ $$-1$$
$$3$$ $$-1$$
$$19$$ $$-1$$

## 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 2736.2.a.v 1
3.b odd 2 1 912.2.a.g 1
4.b odd 2 1 171.2.a.d 1
12.b even 2 1 57.2.a.a 1
20.d odd 2 1 4275.2.a.b 1
24.f even 2 1 3648.2.a.bh 1
24.h odd 2 1 3648.2.a.r 1
28.d even 2 1 8379.2.a.p 1
60.h even 2 1 1425.2.a.j 1
60.l odd 4 2 1425.2.c.b 2
76.d even 2 1 3249.2.a.b 1
84.h odd 2 1 2793.2.a.b 1
132.d odd 2 1 6897.2.a.f 1
156.h even 2 1 9633.2.a.o 1
228.b odd 2 1 1083.2.a.e 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
57.2.a.a 1 12.b even 2 1
171.2.a.d 1 4.b odd 2 1
912.2.a.g 1 3.b odd 2 1
1083.2.a.e 1 228.b odd 2 1
1425.2.a.j 1 60.h even 2 1
1425.2.c.b 2 60.l odd 4 2
2736.2.a.v 1 1.a even 1 1 trivial
2793.2.a.b 1 84.h odd 2 1
3249.2.a.b 1 76.d even 2 1
3648.2.a.r 1 24.h odd 2 1
3648.2.a.bh 1 24.f even 2 1
4275.2.a.b 1 20.d odd 2 1
6897.2.a.f 1 132.d odd 2 1
8379.2.a.p 1 28.d even 2 1
9633.2.a.o 1 156.h even 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2736))$$:

 $$T_{5} - 3$$ $$T_{7} - 5$$ $$T_{11} - 1$$ $$T_{13} - 2$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T$$
$5$ $$-3 + T$$
$7$ $$-5 + T$$
$11$ $$-1 + T$$
$13$ $$-2 + T$$
$17$ $$-1 + T$$
$19$ $$-1 + T$$
$23$ $$4 + T$$
$29$ $$-2 + T$$
$31$ $$-6 + T$$
$37$ $$T$$
$41$ $$T$$
$43$ $$-1 + T$$
$47$ $$9 + T$$
$53$ $$10 + T$$
$59$ $$8 + T$$
$61$ $$1 + T$$
$67$ $$8 + T$$
$71$ $$12 + T$$
$73$ $$11 + T$$
$79$ $$16 + T$$
$83$ $$-12 + T$$
$89$ $$-6 + T$$
$97$ $$10 + T$$