# Properties

 Label 2880.2.a.bd 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 360) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{5} + 2q^{7} + O(q^{10})$$ $$q + q^{5} + 2q^{7} - 2q^{11} - 4q^{13} - 2q^{17} - 4q^{19} + 8q^{23} + q^{25} + 10q^{29} + 4q^{31} + 2q^{35} + 8q^{43} + 8q^{47} - 3q^{49} - 6q^{53} - 2q^{55} + 14q^{59} + 14q^{61} - 4q^{65} + 4q^{67} + 12q^{71} + 6q^{73} - 4q^{77} - 12q^{79} - 4q^{83} - 2q^{85} - 12q^{89} - 8q^{91} - 4q^{95} - 14q^{97} + O(q^{100})$$

## 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

## 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.bd 1
3.b odd 2 1 2880.2.a.n 1
4.b odd 2 1 2880.2.a.w 1
8.b even 2 1 360.2.a.c 1
8.d odd 2 1 720.2.a.a 1
12.b even 2 1 2880.2.a.e 1
24.f even 2 1 720.2.a.i 1
24.h odd 2 1 360.2.a.d yes 1
40.e odd 2 1 3600.2.a.bd 1
40.f even 2 1 1800.2.a.i 1
40.i odd 4 2 1800.2.f.h 2
40.k even 4 2 3600.2.f.g 2
72.j odd 6 2 3240.2.q.d 2
72.n even 6 2 3240.2.q.n 2
120.i odd 2 1 1800.2.a.f 1
120.m even 2 1 3600.2.a.bh 1
120.q odd 4 2 3600.2.f.q 2
120.w even 4 2 1800.2.f.d 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
360.2.a.c 1 8.b even 2 1
360.2.a.d yes 1 24.h odd 2 1
720.2.a.a 1 8.d odd 2 1
720.2.a.i 1 24.f even 2 1
1800.2.a.f 1 120.i odd 2 1
1800.2.a.i 1 40.f even 2 1
1800.2.f.d 2 120.w even 4 2
1800.2.f.h 2 40.i odd 4 2
2880.2.a.e 1 12.b even 2 1
2880.2.a.n 1 3.b odd 2 1
2880.2.a.w 1 4.b odd 2 1
2880.2.a.bd 1 1.a even 1 1 trivial
3240.2.q.d 2 72.j odd 6 2
3240.2.q.n 2 72.n even 6 2
3600.2.a.bd 1 40.e odd 2 1
3600.2.a.bh 1 120.m even 2 1
3600.2.f.g 2 40.k even 4 2
3600.2.f.q 2 120.q odd 4 2

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$3$$ $$1$$
$$5$$ $$-1$$

## Hecke kernels

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

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

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 
$3$ 
$5$ $$1 - T$$
$7$ $$1 - 2 T + 7 T^{2}$$
$11$ $$1 + 2 T + 11 T^{2}$$
$13$ $$1 + 4 T + 13 T^{2}$$
$17$ $$1 + 2 T + 17 T^{2}$$
$19$ $$1 + 4 T + 19 T^{2}$$
$23$ $$1 - 8 T + 23 T^{2}$$
$29$ $$1 - 10 T + 29 T^{2}$$
$31$ $$1 - 4 T + 31 T^{2}$$
$37$ $$1 + 37 T^{2}$$
$41$ $$1 + 41 T^{2}$$
$43$ $$1 - 8 T + 43 T^{2}$$
$47$ $$1 - 8 T + 47 T^{2}$$
$53$ $$1 + 6 T + 53 T^{2}$$
$59$ $$1 - 14 T + 59 T^{2}$$
$61$ $$1 - 14 T + 61 T^{2}$$
$67$ $$1 - 4 T + 67 T^{2}$$
$71$ $$1 - 12 T + 71 T^{2}$$
$73$ $$1 - 6 T + 73 T^{2}$$
$79$ $$1 + 12 T + 79 T^{2}$$
$83$ $$1 + 4 T + 83 T^{2}$$
$89$ $$1 + 12 T + 89 T^{2}$$
$97$ $$1 + 14 T + 97 T^{2}$$