Properties

 Label 570.2.a.j Level $570$ Weight $2$ Character orbit 570.a Self dual yes Analytic conductor $4.551$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ 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

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9}+O(q^{10})$$ q + q^2 + q^3 + q^4 - q^5 + q^6 + 2 * q^7 + q^8 + q^9 $$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} + 6 q^{13} + 2 q^{14} - q^{15} + q^{16} + 4 q^{17} + q^{18} + q^{19} - q^{20} + 2 q^{21} - 4 q^{22} + q^{24} + q^{25} + 6 q^{26} + q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 2 q^{31} + q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} + q^{36} - 2 q^{37} + q^{38} + 6 q^{39} - q^{40} + 8 q^{41} + 2 q^{42} - 8 q^{43} - 4 q^{44} - q^{45} + q^{48} - 3 q^{49} + q^{50} + 4 q^{51} + 6 q^{52} - 6 q^{53} + q^{54} + 4 q^{55} + 2 q^{56} + q^{57} - 10 q^{58} - 2 q^{59} - q^{60} + 2 q^{61} - 2 q^{62} + 2 q^{63} + q^{64} - 6 q^{65} - 4 q^{66} + 4 q^{67} + 4 q^{68} - 2 q^{70} + q^{72} - 10 q^{73} - 2 q^{74} + q^{75} + q^{76} - 8 q^{77} + 6 q^{78} - 2 q^{79} - q^{80} + q^{81} + 8 q^{82} - 10 q^{83} + 2 q^{84} - 4 q^{85} - 8 q^{86} - 10 q^{87} - 4 q^{88} - 12 q^{89} - q^{90} + 12 q^{91} - 2 q^{93} - q^{95} + q^{96} - 2 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100})$$ q + q^2 + q^3 + q^4 - q^5 + q^6 + 2 * q^7 + q^8 + q^9 - q^10 - 4 * q^11 + q^12 + 6 * q^13 + 2 * q^14 - q^15 + q^16 + 4 * q^17 + q^18 + q^19 - q^20 + 2 * q^21 - 4 * q^22 + q^24 + q^25 + 6 * q^26 + q^27 + 2 * q^28 - 10 * q^29 - q^30 - 2 * q^31 + q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 + q^36 - 2 * q^37 + q^38 + 6 * q^39 - q^40 + 8 * q^41 + 2 * q^42 - 8 * q^43 - 4 * q^44 - q^45 + q^48 - 3 * q^49 + q^50 + 4 * q^51 + 6 * q^52 - 6 * q^53 + q^54 + 4 * q^55 + 2 * q^56 + q^57 - 10 * q^58 - 2 * q^59 - q^60 + 2 * q^61 - 2 * q^62 + 2 * q^63 + q^64 - 6 * q^65 - 4 * q^66 + 4 * q^67 + 4 * q^68 - 2 * q^70 + q^72 - 10 * q^73 - 2 * q^74 + q^75 + q^76 - 8 * q^77 + 6 * q^78 - 2 * q^79 - q^80 + q^81 + 8 * q^82 - 10 * q^83 + 2 * q^84 - 4 * q^85 - 8 * q^86 - 10 * q^87 - 4 * q^88 - 12 * q^89 - q^90 + 12 * q^91 - 2 * q^93 - q^95 + q^96 - 2 * q^97 - 3 * q^98 - 4 * q^99

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 1.00000 1.00000 −1.00000 1.00000 2.00000 1.00000 1.00000 −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
$$2$$ $$-1$$
$$3$$ $$-1$$
$$5$$ $$1$$
$$19$$ $$-1$$

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 570.2.a.j 1
3.b odd 2 1 1710.2.a.k 1
4.b odd 2 1 4560.2.a.d 1
5.b even 2 1 2850.2.a.b 1
5.c odd 4 2 2850.2.d.l 2
15.d odd 2 1 8550.2.a.w 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
570.2.a.j 1 1.a even 1 1 trivial
1710.2.a.k 1 3.b odd 2 1
2850.2.a.b 1 5.b even 2 1
2850.2.d.l 2 5.c odd 4 2
4560.2.a.d 1 4.b odd 2 1
8550.2.a.w 1 15.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(570))$$:

 $$T_{7} - 2$$ T7 - 2 $$T_{11} + 4$$ T11 + 4 $$T_{13} - 6$$ T13 - 6

Hecke characteristic polynomials

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