# Properties

 Label 5400.2.a.e Level $5400$ Weight $2$ Character orbit 5400.a Self dual yes Analytic conductor $43.119$ Analytic rank $0$ 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: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 216) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q - 3 q^{7} + O(q^{10})$$ $$q - 3 q^{7} - 5 q^{11} - 4 q^{13} - 8 q^{17} + 2 q^{19} + 2 q^{23} - 6 q^{29} - 7 q^{31} + 6 q^{37} + 6 q^{41} + 2 q^{43} + 6 q^{47} + 2 q^{49} + 5 q^{53} + 4 q^{59} - 8 q^{61} + 10 q^{67} + 8 q^{71} - q^{73} + 15 q^{77} + 16 q^{79} - 11 q^{83} - 6 q^{89} + 12 q^{91} + q^{97} + O(q^{100})$$

## 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 −3.00000 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.e 1
3.b odd 2 1 5400.2.a.h 1
5.b even 2 1 216.2.a.c yes 1
5.c odd 4 2 5400.2.f.b 2
15.d odd 2 1 216.2.a.b 1
15.e even 4 2 5400.2.f.z 2
20.d odd 2 1 432.2.a.f 1
40.e odd 2 1 1728.2.a.i 1
40.f even 2 1 1728.2.a.l 1
45.h odd 6 2 648.2.i.e 2
45.j even 6 2 648.2.i.c 2
60.h even 2 1 432.2.a.c 1
120.i odd 2 1 1728.2.a.s 1
120.m even 2 1 1728.2.a.r 1
180.n even 6 2 1296.2.i.l 2
180.p odd 6 2 1296.2.i.g 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
216.2.a.b 1 15.d odd 2 1
216.2.a.c yes 1 5.b even 2 1
432.2.a.c 1 60.h even 2 1
432.2.a.f 1 20.d odd 2 1
648.2.i.c 2 45.j even 6 2
648.2.i.e 2 45.h odd 6 2
1296.2.i.g 2 180.p odd 6 2
1296.2.i.l 2 180.n even 6 2
1728.2.a.i 1 40.e odd 2 1
1728.2.a.l 1 40.f even 2 1
1728.2.a.r 1 120.m even 2 1
1728.2.a.s 1 120.i odd 2 1
5400.2.a.e 1 1.a even 1 1 trivial
5400.2.a.h 1 3.b odd 2 1
5400.2.f.b 2 5.c odd 4 2
5400.2.f.z 2 15.e even 4 2

## Hecke kernels

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

 $$T_{7} + 3$$ $$T_{11} + 5$$ $$T_{13} + 4$$ $$T_{17} + 8$$

## Hecke characteristic polynomials

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