Properties

 Label 5400.2.a.j Level $5400$ Weight $2$ Character orbit 5400.a Self dual yes Analytic conductor $43.119$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5400 = 2^{3} \cdot 3^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5400.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$43.1192170915$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1080) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - 2q^{7} + O(q^{10})$$ $$q - 2q^{7} - 4q^{11} + 2q^{13} + 5q^{17} - 5q^{19} + q^{23} + 2q^{29} + 7q^{31} + 6q^{37} - 4q^{43} + 4q^{47} - 3q^{49} + 9q^{53} - 14q^{59} - 11q^{61} - 14q^{67} + 12q^{73} + 8q^{77} - 3q^{79} - q^{83} - 4q^{91} - 16q^{97} + O(q^{100})$$

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 0 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 5400.2.a.j 1
3.b odd 2 1 5400.2.a.q 1
5.b even 2 1 1080.2.a.e 1
5.c odd 4 2 5400.2.f.f 2
15.d odd 2 1 1080.2.a.l yes 1
15.e even 4 2 5400.2.f.x 2
20.d odd 2 1 2160.2.a.e 1
40.e odd 2 1 8640.2.a.bi 1
40.f even 2 1 8640.2.a.cd 1
45.h odd 6 2 3240.2.q.b 2
45.j even 6 2 3240.2.q.p 2
60.h even 2 1 2160.2.a.m 1
120.i odd 2 1 8640.2.a.t 1
120.m even 2 1 8640.2.a.k 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1080.2.a.e 1 5.b even 2 1
1080.2.a.l yes 1 15.d odd 2 1
2160.2.a.e 1 20.d odd 2 1
2160.2.a.m 1 60.h even 2 1
3240.2.q.b 2 45.h odd 6 2
3240.2.q.p 2 45.j even 6 2
5400.2.a.j 1 1.a even 1 1 trivial
5400.2.a.q 1 3.b odd 2 1
5400.2.f.f 2 5.c odd 4 2
5400.2.f.x 2 15.e even 4 2
8640.2.a.k 1 120.m even 2 1
8640.2.a.t 1 120.i odd 2 1
8640.2.a.bi 1 40.e odd 2 1
8640.2.a.cd 1 40.f even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5400))$$:

 $$T_{7} + 2$$ $$T_{11} + 4$$ $$T_{13} - 2$$ $$T_{17} - 5$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T$$
$5$ $$T$$
$7$ $$2 + T$$
$11$ $$4 + T$$
$13$ $$-2 + T$$
$17$ $$-5 + T$$
$19$ $$5 + T$$
$23$ $$-1 + T$$
$29$ $$-2 + T$$
$31$ $$-7 + T$$
$37$ $$-6 + T$$
$41$ $$T$$
$43$ $$4 + T$$
$47$ $$-4 + T$$
$53$ $$-9 + T$$
$59$ $$14 + T$$
$61$ $$11 + T$$
$67$ $$14 + T$$
$71$ $$T$$
$73$ $$-12 + T$$
$79$ $$3 + T$$
$83$ $$1 + T$$
$89$ $$T$$
$97$ $$16 + T$$