Properties

 Label 5292.2.a.i Level $5292$ Weight $2$ Character orbit 5292.a Self dual yes Analytic conductor $42.257$ Analytic rank $1$ Dimension $1$ CM discriminant -3 Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5292 = 2^{2} \cdot 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5292.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$42.2568327497$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 756) Fricke sign: $$1$$ Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + O(q^{10})$$ $$q + 7 q^{13} - 8 q^{19} - 5 q^{25} - 11 q^{31} - q^{37} - 13 q^{43} + q^{61} + 11 q^{67} + 10 q^{73} - 13 q^{79} + 19 q^{97} + O(q^{100})$$

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 0 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
$$2$$ $$-1$$
$$3$$ $$1$$
$$7$$ $$-1$$

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 CM by $$\Q(\sqrt{-3})$$

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5292.2.a.i 1
3.b odd 2 1 CM 5292.2.a.i 1
7.b odd 2 1 5292.2.a.d 1
7.d odd 6 2 756.2.k.a 2
21.c even 2 1 5292.2.a.d 1
21.g even 6 2 756.2.k.a 2
63.i even 6 2 2268.2.i.e 2
63.k odd 6 2 2268.2.l.f 2
63.s even 6 2 2268.2.l.f 2
63.t odd 6 2 2268.2.i.e 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
756.2.k.a 2 7.d odd 6 2
756.2.k.a 2 21.g even 6 2
2268.2.i.e 2 63.i even 6 2
2268.2.i.e 2 63.t odd 6 2
2268.2.l.f 2 63.k odd 6 2
2268.2.l.f 2 63.s even 6 2
5292.2.a.d 1 7.b odd 2 1
5292.2.a.d 1 21.c even 2 1
5292.2.a.i 1 1.a even 1 1 trivial
5292.2.a.i 1 3.b odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5292))$$:

 $$T_{5}$$ $$T_{11}$$ $$T_{13} - 7$$ $$T_{17}$$ $$T_{19} + 8$$

Hecke characteristic polynomials

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