Properties

 Label 8550.2.a.c Level $8550$ Weight $2$ Character orbit 8550.a Self dual yes Analytic conductor $68.272$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 8550.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$68.2720937282$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 2850) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{4} - 4q^{7} - q^{8} + O(q^{10})$$ $$q - q^{2} + q^{4} - 4q^{7} - q^{8} + q^{11} + 4q^{14} + q^{16} + 8q^{17} + q^{19} - q^{22} + 3q^{23} - 4q^{28} + q^{29} + q^{31} - q^{32} - 8q^{34} - 2q^{37} - q^{38} + 10q^{41} - 8q^{43} + q^{44} - 3q^{46} + 9q^{49} - 3q^{53} + 4q^{56} - q^{58} - 4q^{59} + 5q^{61} - q^{62} + q^{64} - 5q^{67} + 8q^{68} + 6q^{71} - 13q^{73} + 2q^{74} + q^{76} - 4q^{77} - 5q^{79} - 10q^{82} - 11q^{83} + 8q^{86} - q^{88} - 3q^{89} + 3q^{92} + 10q^{97} - 9q^{98} + O(q^{100})$$

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 0 0 −4.00000 −1.00000 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
$$2$$ $$1$$
$$3$$ $$-1$$
$$5$$ $$-1$$
$$19$$ $$-1$$

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 8550.2.a.c 1
3.b odd 2 1 2850.2.a.w yes 1
5.b even 2 1 8550.2.a.bk 1
15.d odd 2 1 2850.2.a.f 1
15.e even 4 2 2850.2.d.o 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2850.2.a.f 1 15.d odd 2 1
2850.2.a.w yes 1 3.b odd 2 1
2850.2.d.o 2 15.e even 4 2
8550.2.a.c 1 1.a even 1 1 trivial
8550.2.a.bk 1 5.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 $$S_{2}^{\mathrm{new}}(\Gamma_0(8550))$$:

 $$T_{7} + 4$$ $$T_{11} - 1$$ $$T_{13}$$ $$T_{17} - 8$$ $$T_{23} - 3$$ $$T_{53} + 3$$

Hecke characteristic polynomials

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