Properties

 Label 5390.2.a.i Level $5390$ Weight $2$ Character orbit 5390.a Self dual yes Analytic conductor $43.039$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5390.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$43.0393666895$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 770) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{4} - q^{5} - q^{8} - 3q^{9} + O(q^{10})$$ $$q - q^{2} + q^{4} - q^{5} - q^{8} - 3q^{9} + q^{10} - q^{11} - 2q^{13} + q^{16} - 6q^{17} + 3q^{18} - 4q^{19} - q^{20} + q^{22} + 4q^{23} + q^{25} + 2q^{26} - 2q^{29} - 8q^{31} - q^{32} + 6q^{34} - 3q^{36} - 10q^{37} + 4q^{38} + q^{40} + 6q^{41} + 12q^{43} - q^{44} + 3q^{45} - 4q^{46} - 12q^{47} - q^{50} - 2q^{52} + 6q^{53} + q^{55} + 2q^{58} + 12q^{59} - 6q^{61} + 8q^{62} + q^{64} + 2q^{65} + 8q^{67} - 6q^{68} - 8q^{71} + 3q^{72} - 14q^{73} + 10q^{74} - 4q^{76} - q^{80} + 9q^{81} - 6q^{82} - 4q^{83} + 6q^{85} - 12q^{86} + q^{88} + 6q^{89} - 3q^{90} + 4q^{92} + 12q^{94} + 4q^{95} + 14q^{97} + 3q^{99} + O(q^{100})$$

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
−1.00000 0 1.00000 −1.00000 0 0 −1.00000 −3.00000 1.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$5$$ $$1$$
$$7$$ $$-1$$
$$11$$ $$1$$

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 5390.2.a.i 1
7.b odd 2 1 770.2.a.c 1
21.c even 2 1 6930.2.a.u 1
28.d even 2 1 6160.2.a.i 1
35.c odd 2 1 3850.2.a.t 1
35.f even 4 2 3850.2.c.h 2
77.b even 2 1 8470.2.a.ba 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
770.2.a.c 1 7.b odd 2 1
3850.2.a.t 1 35.c odd 2 1
3850.2.c.h 2 35.f even 4 2
5390.2.a.i 1 1.a even 1 1 trivial
6160.2.a.i 1 28.d even 2 1
6930.2.a.u 1 21.c even 2 1
8470.2.a.ba 1 77.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5390))$$:

 $$T_{3}$$ $$T_{13} + 2$$ $$T_{17} + 6$$ $$T_{19} + 4$$ $$T_{31} + 8$$

Hecke characteristic polynomials

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