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Properties

Label 1760.2.g.c
Level $1760$
Weight $2$
Character orbit 1760.g
Analytic conductor $14.054$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1760,2,Mod(881,1760)] 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([0, 1, 0, 0])) 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("1760.881"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1760.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24] 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: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 40 q^{9} + 4 q^{15} + 28 q^{17} - 12 q^{23} - 24 q^{25} - 8 q^{31} + 4 q^{33} + 24 q^{39} - 40 q^{41} + 20 q^{47} + 64 q^{49} - 24 q^{55} - 56 q^{57} - 40 q^{63} + 20 q^{65} - 24 q^{71} - 36 q^{73}+ \cdots + 48 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
881.1 0 − 3.34174i 0 1.00000i 0 −0.333306 0 −8.16722 0
881.2 0 − 3.33890i 0 − 1.00000i 0 3.21725 0 −8.14826 0
881.3 0 − 2.93797i 0 1.00000i 0 4.84749 0 −5.63167 0
881.4 0 − 2.73124i 0 − 1.00000i 0 −4.25690 0 −4.45970 0
881.5 0 − 2.28755i 0 1.00000i 0 −2.08702 0 −2.23288 0
881.6 0 − 2.08501i 0 1.00000i 0 −2.28761 0 −1.34727 0
881.7 0 − 1.82409i 0 − 1.00000i 0 3.30914 0 −0.327312 0
881.8 0 − 1.41634i 0 1.00000i 0 −4.34669 0 0.993975 0
881.9 0 − 1.29586i 0 − 1.00000i 0 −1.35877 0 1.32075 0
881.10 0 − 0.894414i 0 − 1.00000i 0 −2.43095 0 2.20002 0
881.11 0 − 0.324436i 0 1.00000i 0 2.45816 0 2.89474 0
881.12 0 − 0.308537i 0 − 1.00000i 0 3.26920 0 2.90480 0
881.13 0 0.308537i 0 1.00000i 0 3.26920 0 2.90480 0
881.14 0 0.324436i 0 − 1.00000i 0 2.45816 0 2.89474 0
881.15 0 0.894414i 0 1.00000i 0 −2.43095 0 2.20002 0
881.16 0 1.29586i 0 1.00000i 0 −1.35877 0 1.32075 0
881.17 0 1.41634i 0 − 1.00000i 0 −4.34669 0 0.993975 0
881.18 0 1.82409i 0 1.00000i 0 3.30914 0 −0.327312 0
881.19 0 2.08501i 0 − 1.00000i 0 −2.28761 0 −1.34727 0
881.20 0 2.28755i 0 − 1.00000i 0 −2.08702 0 −2.23288 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 881.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.b 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.g.c 24
4.b odd 2 1 440.2.g.c ✓ 24
8.b even 2 1 inner 1760.2.g.c 24
8.d odd 2 1 440.2.g.c ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
440.2.g.c ✓ 24 4.b odd 2 1
440.2.g.c ✓ 24 8.d odd 2 1
1760.2.g.c 24 1.a even 1 1 trivial
1760.2.g.c 24 8.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} + 56 T_{3}^{22} + 1346 T_{3}^{20} + 18208 T_{3}^{18} + 152849 T_{3}^{16} + 828472 T_{3}^{14} + \cdots + 16384 \) acting on \(S_{2}^{\mathrm{new}}(1760, [\chi])\). Copy content Toggle raw display