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Properties

Label 1760.2.c.c
Level $1760$
Weight $2$
Character orbit 1760.c
Analytic conductor $14.054$
Analytic rank $0$
Dimension $56$
Inner twists $8$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1760,2,Mod(879,1760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1760.879"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1760.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.0536707557\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: no (minimal twist has level 440)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 104 q^{9} + 16 q^{25} + 8 q^{49} - 96 q^{59} + 24 q^{75} - 56 q^{81} - 64 q^{89} - 32 q^{91} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
879.1 0 − 3.03912i 0 −2.09783 − 0.774024i 0 1.67292i 0 −6.23628 0
879.2 0 3.03912i 0 −2.09783 + 0.774024i 0 − 1.67292i 0 −6.23628 0
879.3 0 − 2.36305i 0 1.64789 − 1.51144i 0 2.95047i 0 −2.58400 0
879.4 0 2.36305i 0 1.64789 + 1.51144i 0 − 2.95047i 0 −2.58400 0
879.5 0 − 1.93862i 0 2.16613 + 0.554857i 0 3.35344i 0 −0.758244 0
879.6 0 1.93862i 0 2.16613 − 0.554857i 0 − 3.35344i 0 −0.758244 0
879.7 0 − 2.36305i 0 1.64789 − 1.51144i 0 − 2.95047i 0 −2.58400 0
879.8 0 2.36305i 0 1.64789 + 1.51144i 0 2.95047i 0 −2.58400 0
879.9 0 − 1.93054i 0 −0.651439 + 2.13907i 0 − 0.116559i 0 −0.727003 0
879.10 0 1.93054i 0 −0.651439 − 2.13907i 0 0.116559i 0 −0.727003 0
879.11 0 − 3.03912i 0 2.09783 + 0.774024i 0 − 1.67292i 0 −6.23628 0
879.12 0 3.03912i 0 2.09783 − 0.774024i 0 1.67292i 0 −6.23628 0
879.13 0 − 3.06894i 0 0.514972 + 2.17596i 0 3.58937i 0 −6.41839 0
879.14 0 3.06894i 0 0.514972 − 2.17596i 0 − 3.58937i 0 −6.41839 0
879.15 0 − 1.93862i 0 2.16613 + 0.554857i 0 − 3.35344i 0 −0.758244 0
879.16 0 1.93862i 0 2.16613 − 0.554857i 0 3.35344i 0 −0.758244 0
879.17 0 − 1.93054i 0 0.651439 − 2.13907i 0 0.116559i 0 −0.727003 0
879.18 0 1.93054i 0 0.651439 + 2.13907i 0 − 0.116559i 0 −0.727003 0
879.19 0 − 1.20551i 0 −1.79732 + 1.33028i 0 3.49920i 0 1.54674 0
879.20 0 1.20551i 0 −1.79732 − 1.33028i 0 − 3.49920i 0 1.54674 0
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 879.56
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
8.d odd 2 1 inner
11.b odd 2 1 inner
40.e odd 2 1 inner
55.d odd 2 1 inner
88.g even 2 1 inner
440.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1760.2.c.c 56
4.b odd 2 1 440.2.c.c ✓ 56
5.b even 2 1 inner 1760.2.c.c 56
8.b even 2 1 440.2.c.c ✓ 56
8.d odd 2 1 inner 1760.2.c.c 56
11.b odd 2 1 inner 1760.2.c.c 56
20.d odd 2 1 440.2.c.c ✓ 56
40.e odd 2 1 inner 1760.2.c.c 56
40.f even 2 1 440.2.c.c ✓ 56
44.c even 2 1 440.2.c.c ✓ 56
55.d odd 2 1 inner 1760.2.c.c 56
88.b odd 2 1 440.2.c.c ✓ 56
88.g even 2 1 inner 1760.2.c.c 56
220.g even 2 1 440.2.c.c ✓ 56
440.c even 2 1 inner 1760.2.c.c 56
440.o odd 2 1 440.2.c.c ✓ 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
440.2.c.c ✓ 56 4.b odd 2 1
440.2.c.c ✓ 56 8.b even 2 1
440.2.c.c ✓ 56 20.d odd 2 1
440.2.c.c ✓ 56 40.f even 2 1
440.2.c.c ✓ 56 44.c even 2 1
440.2.c.c ✓ 56 88.b odd 2 1
440.2.c.c ✓ 56 220.g even 2 1
440.2.c.c ✓ 56 440.o odd 2 1
1760.2.c.c 56 1.a even 1 1 trivial
1760.2.c.c 56 5.b even 2 1 inner
1760.2.c.c 56 8.d odd 2 1 inner
1760.2.c.c 56 11.b odd 2 1 inner
1760.2.c.c 56 40.e odd 2 1 inner
1760.2.c.c 56 55.d odd 2 1 inner
1760.2.c.c 56 88.g even 2 1 inner
1760.2.c.c 56 440.c even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1760, [\chi])\):

\( T_{3}^{14} + 34T_{3}^{12} + 460T_{3}^{10} + 3174T_{3}^{8} + 11911T_{3}^{6} + 23872T_{3}^{4} + 23036T_{3}^{2} + 8136 \) Copy content Toggle raw display
\( T_{7}^{14} + 48T_{7}^{12} + 889T_{7}^{10} + 7834T_{7}^{8} + 32084T_{7}^{6} + 47048T_{7}^{4} + 5344T_{7}^{2} + 64 \) Copy content Toggle raw display