Properties

Label 160.6.f.a
Level 160
Weight 6
Character orbit 160.f
Analytic conductor 25.661
Analytic rank 0
Dimension 28
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.6614111701\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 28q + 1940q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 28q + 1940q^{9} + 488q^{15} + 1556q^{25} - 4368q^{31} - 23360q^{39} - 2480q^{41} - 38420q^{49} + 48776q^{55} + 37200q^{65} + 69232q^{71} + 35984q^{79} + 122596q^{81} - 178744q^{89} - 89416q^{95} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
49.1 0 −28.9041 0 −40.5064 38.5257i 0 128.100i 0 592.448 0
49.2 0 −28.9041 0 −40.5064 + 38.5257i 0 128.100i 0 592.448 0
49.3 0 −21.6833 0 36.8367 42.0483i 0 236.448i 0 227.167 0
49.4 0 −21.6833 0 36.8367 + 42.0483i 0 236.448i 0 227.167 0
49.5 0 −21.4357 0 48.3867 + 27.9951i 0 39.9262i 0 216.491 0
49.6 0 −21.4357 0 48.3867 27.9951i 0 39.9262i 0 216.491 0
49.7 0 −16.0077 0 −19.1184 + 52.5308i 0 20.5525i 0 13.2465 0
49.8 0 −16.0077 0 −19.1184 52.5308i 0 20.5525i 0 13.2465 0
49.9 0 −10.5561 0 −52.7686 18.4521i 0 47.9937i 0 −131.568 0
49.10 0 −10.5561 0 −52.7686 + 18.4521i 0 47.9937i 0 −131.568 0
49.11 0 −7.17847 0 1.28331 + 55.8870i 0 146.905i 0 −191.470 0
49.12 0 −7.17847 0 1.28331 55.8870i 0 146.905i 0 −191.470 0
49.13 0 −1.29818 0 51.3939 21.9924i 0 170.399i 0 −241.315 0
49.14 0 −1.29818 0 51.3939 + 21.9924i 0 170.399i 0 −241.315 0
49.15 0 1.29818 0 −51.3939 + 21.9924i 0 170.399i 0 −241.315 0
49.16 0 1.29818 0 −51.3939 21.9924i 0 170.399i 0 −241.315 0
49.17 0 7.17847 0 −1.28331 55.8870i 0 146.905i 0 −191.470 0
49.18 0 7.17847 0 −1.28331 + 55.8870i 0 146.905i 0 −191.470 0
49.19 0 10.5561 0 52.7686 + 18.4521i 0 47.9937i 0 −131.568 0
49.20 0 10.5561 0 52.7686 18.4521i 0 47.9937i 0 −131.568 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 49.28
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
8.b even 2 1 inner
40.f even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 160.6.f.a 28
4.b odd 2 1 40.6.f.a 28
5.b even 2 1 inner 160.6.f.a 28
5.c odd 4 2 800.6.d.e 28
8.b even 2 1 inner 160.6.f.a 28
8.d odd 2 1 40.6.f.a 28
20.d odd 2 1 40.6.f.a 28
20.e even 4 2 200.6.d.e 28
40.e odd 2 1 40.6.f.a 28
40.f even 2 1 inner 160.6.f.a 28
40.i odd 4 2 800.6.d.e 28
40.k even 4 2 200.6.d.e 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
40.6.f.a 28 4.b odd 2 1
40.6.f.a 28 8.d odd 2 1
40.6.f.a 28 20.d odd 2 1
40.6.f.a 28 40.e odd 2 1
160.6.f.a 28 1.a even 1 1 trivial
160.6.f.a 28 5.b even 2 1 inner
160.6.f.a 28 8.b even 2 1 inner
160.6.f.a 28 40.f even 2 1 inner
200.6.d.e 28 20.e even 4 2
200.6.d.e 28 40.k even 4 2
800.6.d.e 28 5.c odd 4 2
800.6.d.e 28 40.i odd 4 2

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(160, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database