# Properties

 Label 6018.2.a.l Level $6018$ Weight $2$ Character orbit 6018.a Self dual yes Analytic conductor $48.054$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$6018 = 2 \cdot 3 \cdot 17 \cdot 59$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6018.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$48.0539719364$$ 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

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + 2q^{10} + 4q^{11} + q^{12} - 2q^{13} - 4q^{14} + 2q^{15} + q^{16} + q^{17} + q^{18} - 4q^{19} + 2q^{20} - 4q^{21} + 4q^{22} + 4q^{23} + q^{24} - q^{25} - 2q^{26} + q^{27} - 4q^{28} + 10q^{29} + 2q^{30} + 4q^{31} + q^{32} + 4q^{33} + q^{34} - 8q^{35} + q^{36} + 2q^{37} - 4q^{38} - 2q^{39} + 2q^{40} - 6q^{41} - 4q^{42} + 12q^{43} + 4q^{44} + 2q^{45} + 4q^{46} - 8q^{47} + q^{48} + 9q^{49} - q^{50} + q^{51} - 2q^{52} + 6q^{53} + q^{54} + 8q^{55} - 4q^{56} - 4q^{57} + 10q^{58} - q^{59} + 2q^{60} + 10q^{61} + 4q^{62} - 4q^{63} + q^{64} - 4q^{65} + 4q^{66} - 4q^{67} + q^{68} + 4q^{69} - 8q^{70} - 12q^{71} + q^{72} + 10q^{73} + 2q^{74} - q^{75} - 4q^{76} - 16q^{77} - 2q^{78} + 12q^{79} + 2q^{80} + q^{81} - 6q^{82} + 12q^{83} - 4q^{84} + 2q^{85} + 12q^{86} + 10q^{87} + 4q^{88} + 10q^{89} + 2q^{90} + 8q^{91} + 4q^{92} + 4q^{93} - 8q^{94} - 8q^{95} + q^{96} + 10q^{97} + 9q^{98} + 4q^{99} + O(q^{100})$$

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

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$-1$$
$$3$$ $$-1$$
$$17$$ $$-1$$
$$59$$ $$1$$

## 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 6018.2.a.l 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6018.2.a.l 1 1.a even 1 1 trivial

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(6018))$$:

 $$T_{5} - 2$$ $$T_{7} + 4$$

## Hecke characteristic polynomials

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