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

Downloads

Learn more about

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

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

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:

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(7\) \(-1\)
\(11\) \(-1\)

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

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