Properties

 Label 5082.2.a.a Level $5082$ Weight $2$ Character orbit 5082.a Self dual yes Analytic conductor $40.580$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5082.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$40.5799743072$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 462) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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 −1.00000 1.00000 −4.00000 1.00000 −1.00000 −1.00000 1.00000 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
$$2$$ $$1$$
$$3$$ $$1$$
$$7$$ $$1$$
$$11$$ $$-1$$

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 5082.2.a.a 1
11.b odd 2 1 462.2.a.e 1
33.d even 2 1 1386.2.a.e 1
44.c even 2 1 3696.2.a.p 1
77.b even 2 1 3234.2.a.v 1
231.h odd 2 1 9702.2.a.b 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
462.2.a.e 1 11.b odd 2 1
1386.2.a.e 1 33.d even 2 1
3234.2.a.v 1 77.b even 2 1
3696.2.a.p 1 44.c even 2 1
5082.2.a.a 1 1.a even 1 1 trivial
9702.2.a.b 1 231.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5082))$$:

 $$T_{5} + 4$$ $$T_{13} - 6$$ $$T_{17} - 4$$ $$T_{19} - 2$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T$$
$3$ $$1 + T$$
$5$ $$4 + T$$
$7$ $$1 + T$$
$11$ $$T$$
$13$ $$-6 + T$$
$17$ $$-4 + T$$
$19$ $$-2 + T$$
$23$ $$8 + T$$
$29$ $$-6 + T$$
$31$ $$-6 + T$$
$37$ $$6 + T$$
$41$ $$12 + T$$
$43$ $$4 + T$$
$47$ $$-6 + T$$
$53$ $$-2 + T$$
$59$ $$T$$
$61$ $$10 + T$$
$67$ $$-4 + T$$
$71$ $$12 + T$$
$73$ $$T$$
$79$ $$-16 + T$$
$83$ $$-14 + T$$
$89$ $$14 + T$$
$97$ $$14 + T$$