# Properties

 Label 6017.2.a.b Level 6017 Weight 2 Character orbit 6017.a Self dual yes Analytic conductor 48.046 Analytic rank 0 Dimension 1 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$6017 = 11 \cdot 547$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6017.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$48.0459868962$$ 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

 $$f(q)$$ $$=$$ $$q + 2q^{3} - 2q^{4} + 4q^{5} + 2q^{7} + q^{9} + O(q^{10})$$ $$q + 2q^{3} - 2q^{4} + 4q^{5} + 2q^{7} + q^{9} + q^{11} - 4q^{12} + q^{13} + 8q^{15} + 4q^{16} + 8q^{17} - 5q^{19} - 8q^{20} + 4q^{21} + 6q^{23} + 11q^{25} - 4q^{27} - 4q^{28} + 5q^{29} + 10q^{31} + 2q^{33} + 8q^{35} - 2q^{36} + 2q^{39} - 10q^{43} - 2q^{44} + 4q^{45} - 9q^{47} + 8q^{48} - 3q^{49} + 16q^{51} - 2q^{52} - 10q^{53} + 4q^{55} - 10q^{57} - 14q^{59} - 16q^{60} - 14q^{61} + 2q^{63} - 8q^{64} + 4q^{65} - q^{67} - 16q^{68} + 12q^{69} + 12q^{71} - 2q^{73} + 22q^{75} + 10q^{76} + 2q^{77} + 4q^{79} + 16q^{80} - 11q^{81} + 6q^{83} - 8q^{84} + 32q^{85} + 10q^{87} - 6q^{89} + 2q^{91} - 12q^{92} + 20q^{93} - 20q^{95} - 13q^{97} + q^{99} + O(q^{100})$$

## 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
0 2.00000 −2.00000 4.00000 0 2.00000 0 1.00000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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 6017.2.a.b 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6017.2.a.b 1 1.a even 1 1 trivial

## Atkin-Lehner signs

$$p$$ Sign
$$11$$ $$-1$$
$$547$$ $$1$$

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(6017))$$:

 $$T_{2}$$ $$T_{3} - 2$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 2 T^{2}$$
$3$ $$1 - 2 T + 3 T^{2}$$
$5$ $$1 - 4 T + 5 T^{2}$$
$7$ $$1 - 2 T + 7 T^{2}$$
$11$ $$1 - T$$
$13$ $$1 - T + 13 T^{2}$$
$17$ $$1 - 8 T + 17 T^{2}$$
$19$ $$1 + 5 T + 19 T^{2}$$
$23$ $$1 - 6 T + 23 T^{2}$$
$29$ $$1 - 5 T + 29 T^{2}$$
$31$ $$1 - 10 T + 31 T^{2}$$
$37$ $$1 + 37 T^{2}$$
$41$ $$1 + 41 T^{2}$$
$43$ $$1 + 10 T + 43 T^{2}$$
$47$ $$1 + 9 T + 47 T^{2}$$
$53$ $$1 + 10 T + 53 T^{2}$$
$59$ $$1 + 14 T + 59 T^{2}$$
$61$ $$1 + 14 T + 61 T^{2}$$
$67$ $$1 + T + 67 T^{2}$$
$71$ $$1 - 12 T + 71 T^{2}$$
$73$ $$1 + 2 T + 73 T^{2}$$
$79$ $$1 - 4 T + 79 T^{2}$$
$83$ $$1 - 6 T + 83 T^{2}$$
$89$ $$1 + 6 T + 89 T^{2}$$
$97$ $$1 + 13 T + 97 T^{2}$$