# Properties

 Label 2880.2.a.be Level $2880$ Weight $2$ Character orbit 2880.a Self dual yes Analytic conductor $22.997$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2880 = 2^{6} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2880.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$22.9969157821$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1440) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{5} + 2q^{7} + O(q^{10})$$ $$q + q^{5} + 2q^{7} + 2q^{11} + 2q^{17} - 4q^{19} + q^{25} + 2q^{29} + 8q^{31} + 2q^{35} + 4q^{37} + 8q^{41} - 8q^{43} + 8q^{47} - 3q^{49} + 10q^{53} + 2q^{55} - 6q^{59} - 2q^{61} - 12q^{67} - 12q^{71} - 2q^{73} + 4q^{77} + 8q^{79} - 4q^{83} + 2q^{85} + 12q^{89} - 4q^{95} + 10q^{97} + O(q^{100})$$

## 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 1.00000 0 2.00000 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
$$2$$ $$1$$
$$3$$ $$1$$
$$5$$ $$-1$$

## 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 2880.2.a.be 1
3.b odd 2 1 2880.2.a.l 1
4.b odd 2 1 2880.2.a.v 1
8.b even 2 1 1440.2.a.e yes 1
8.d odd 2 1 1440.2.a.b 1
12.b even 2 1 2880.2.a.g 1
24.f even 2 1 1440.2.a.h yes 1
24.h odd 2 1 1440.2.a.m yes 1
40.e odd 2 1 7200.2.a.bo 1
40.f even 2 1 7200.2.a.m 1
40.i odd 4 2 7200.2.f.h 2
40.k even 4 2 7200.2.f.v 2
120.i odd 2 1 7200.2.a.n 1
120.m even 2 1 7200.2.a.bn 1
120.q odd 4 2 7200.2.f.i 2
120.w even 4 2 7200.2.f.u 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1440.2.a.b 1 8.d odd 2 1
1440.2.a.e yes 1 8.b even 2 1
1440.2.a.h yes 1 24.f even 2 1
1440.2.a.m yes 1 24.h odd 2 1
2880.2.a.g 1 12.b even 2 1
2880.2.a.l 1 3.b odd 2 1
2880.2.a.v 1 4.b odd 2 1
2880.2.a.be 1 1.a even 1 1 trivial
7200.2.a.m 1 40.f even 2 1
7200.2.a.n 1 120.i odd 2 1
7200.2.a.bn 1 120.m even 2 1
7200.2.a.bo 1 40.e odd 2 1
7200.2.f.h 2 40.i odd 4 2
7200.2.f.i 2 120.q odd 4 2
7200.2.f.u 2 120.w even 4 2
7200.2.f.v 2 40.k even 4 2

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2880))$$:

 $$T_{7} - 2$$ $$T_{11} - 2$$ $$T_{13}$$ $$T_{17} - 2$$ $$T_{19} + 4$$

## Hecke characteristic polynomials

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