Properties

 Label 5082.2.a.d Level $5082$ Weight $2$ Character orbit 5082.a Self dual yes Analytic conductor $40.580$ Analytic rank $1$ 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: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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 −2.00000 1.00000 1.00000 −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
$$2$$ $$1$$
$$3$$ $$1$$
$$7$$ $$-1$$
$$11$$ $$-1$$

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.d 1
11.b odd 2 1 42.2.a.a 1
33.d even 2 1 126.2.a.a 1
44.c even 2 1 336.2.a.d 1
55.d odd 2 1 1050.2.a.i 1
55.e even 4 2 1050.2.g.a 2
77.b even 2 1 294.2.a.g 1
77.h odd 6 2 294.2.e.c 2
77.i even 6 2 294.2.e.a 2
88.b odd 2 1 1344.2.a.q 1
88.g even 2 1 1344.2.a.i 1
99.g even 6 2 1134.2.f.j 2
99.h odd 6 2 1134.2.f.g 2
132.d odd 2 1 1008.2.a.j 1
143.d odd 2 1 7098.2.a.f 1
165.d even 2 1 3150.2.a.bo 1
165.l odd 4 2 3150.2.g.r 2
176.i even 4 2 5376.2.c.e 2
176.l odd 4 2 5376.2.c.bc 2
220.g even 2 1 8400.2.a.k 1
231.h odd 2 1 882.2.a.b 1
231.k odd 6 2 882.2.g.j 2
231.l even 6 2 882.2.g.h 2
264.m even 2 1 4032.2.a.e 1
264.p odd 2 1 4032.2.a.m 1
308.g odd 2 1 2352.2.a.l 1
308.m odd 6 2 2352.2.q.n 2
308.n even 6 2 2352.2.q.i 2
385.h even 2 1 7350.2.a.f 1
616.g odd 2 1 9408.2.a.bw 1
616.o even 2 1 9408.2.a.n 1
924.n even 2 1 7056.2.a.k 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
42.2.a.a 1 11.b odd 2 1
126.2.a.a 1 33.d even 2 1
294.2.a.g 1 77.b even 2 1
294.2.e.a 2 77.i even 6 2
294.2.e.c 2 77.h odd 6 2
336.2.a.d 1 44.c even 2 1
882.2.a.b 1 231.h odd 2 1
882.2.g.h 2 231.l even 6 2
882.2.g.j 2 231.k odd 6 2
1008.2.a.j 1 132.d odd 2 1
1050.2.a.i 1 55.d odd 2 1
1050.2.g.a 2 55.e even 4 2
1134.2.f.g 2 99.h odd 6 2
1134.2.f.j 2 99.g even 6 2
1344.2.a.i 1 88.g even 2 1
1344.2.a.q 1 88.b odd 2 1
2352.2.a.l 1 308.g odd 2 1
2352.2.q.i 2 308.n even 6 2
2352.2.q.n 2 308.m odd 6 2
3150.2.a.bo 1 165.d even 2 1
3150.2.g.r 2 165.l odd 4 2
4032.2.a.e 1 264.m even 2 1
4032.2.a.m 1 264.p odd 2 1
5082.2.a.d 1 1.a even 1 1 trivial
5376.2.c.e 2 176.i even 4 2
5376.2.c.bc 2 176.l odd 4 2
7056.2.a.k 1 924.n even 2 1
7098.2.a.f 1 143.d odd 2 1
7350.2.a.f 1 385.h even 2 1
8400.2.a.k 1 220.g even 2 1
9408.2.a.n 1 616.o even 2 1
9408.2.a.bw 1 616.g odd 2 1

Hecke kernels

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

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

Hecke characteristic polynomials

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