# Properties

 Label 574.2.a.j Level $574$ Weight $2$ Character orbit 574.a Self dual yes Analytic conductor $4.583$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$574 = 2 \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 574.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$4.58341307602$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{4} - 4q^{5} + q^{7} + q^{8} - 3q^{9} + O(q^{10})$$ $$q + q^{2} + q^{4} - 4q^{5} + q^{7} + q^{8} - 3q^{9} - 4q^{10} - 2q^{11} - 6q^{13} + q^{14} + q^{16} - 6q^{17} - 3q^{18} + 4q^{19} - 4q^{20} - 2q^{22} + 8q^{23} + 11q^{25} - 6q^{26} + q^{28} - 8q^{29} + q^{32} - 6q^{34} - 4q^{35} - 3q^{36} - 2q^{37} + 4q^{38} - 4q^{40} - q^{41} - 8q^{43} - 2q^{44} + 12q^{45} + 8q^{46} + q^{49} + 11q^{50} - 6q^{52} + 8q^{55} + q^{56} - 8q^{58} + 2q^{59} - 8q^{61} - 3q^{63} + q^{64} + 24q^{65} + 10q^{67} - 6q^{68} - 4q^{70} - 12q^{71} - 3q^{72} + 10q^{73} - 2q^{74} + 4q^{76} - 2q^{77} + 16q^{79} - 4q^{80} + 9q^{81} - q^{82} - 2q^{83} + 24q^{85} - 8q^{86} - 2q^{88} - 10q^{89} + 12q^{90} - 6q^{91} + 8q^{92} - 16q^{95} - 2q^{97} + q^{98} + 6q^{99} + O(q^{100})$$

## 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 −4.00000 0 1.00000 1.00000 −3.00000 −4.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$-1$$
$$7$$ $$-1$$
$$41$$ $$1$$

## 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 574.2.a.j 1
3.b odd 2 1 5166.2.a.t 1
4.b odd 2 1 4592.2.a.f 1
7.b odd 2 1 4018.2.a.n 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.a.j 1 1.a even 1 1 trivial
4018.2.a.n 1 7.b odd 2 1
4592.2.a.f 1 4.b odd 2 1
5166.2.a.t 1 3.b odd 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(574))$$:

 $$T_{3}$$ $$T_{5} + 4$$ $$T_{11} + 2$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$-1 + T$$
$3$ $$T$$
$5$ $$4 + T$$
$7$ $$-1 + T$$
$11$ $$2 + T$$
$13$ $$6 + T$$
$17$ $$6 + T$$
$19$ $$-4 + T$$
$23$ $$-8 + T$$
$29$ $$8 + T$$
$31$ $$T$$
$37$ $$2 + T$$
$41$ $$1 + T$$
$43$ $$8 + T$$
$47$ $$T$$
$53$ $$T$$
$59$ $$-2 + T$$
$61$ $$8 + T$$
$67$ $$-10 + T$$
$71$ $$12 + T$$
$73$ $$-10 + T$$
$79$ $$-16 + T$$
$83$ $$2 + T$$
$89$ $$10 + T$$
$97$ $$2 + T$$