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Properties

Label 5760.2.o.b
Level $5760$
Weight $2$
Character orbit 5760.o
Analytic conductor $45.994$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [5760,2,Mod(5759,5760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5760.5759"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 5760 = 2^{7} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5760.o (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(45.9938315643\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 8 q^{5} + 16 q^{17} + 24 q^{49} - 16 q^{53} + 16 q^{61} + 96 q^{77} + 24 q^{85}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5759.1 0 0 0 −2.22693 − 0.201904i 0 −2.36945 0 0 0
5759.2 0 0 0 −2.22693 − 0.201904i 0 2.36945 0 0 0
5759.3 0 0 0 −2.22693 + 0.201904i 0 −2.36945 0 0 0
5759.4 0 0 0 −2.22693 + 0.201904i 0 2.36945 0 0 0
5759.5 0 0 0 −1.90128 − 1.17692i 0 −4.45014 0 0 0
5759.6 0 0 0 −1.90128 − 1.17692i 0 4.45014 0 0 0
5759.7 0 0 0 −1.90128 + 1.17692i 0 −4.45014 0 0 0
5759.8 0 0 0 −1.90128 + 1.17692i 0 4.45014 0 0 0
5759.9 0 0 0 −1.21685 − 1.87598i 0 −0.176638 0 0 0
5759.10 0 0 0 −1.21685 − 1.87598i 0 0.176638 0 0 0
5759.11 0 0 0 −1.21685 + 1.87598i 0 −0.176638 0 0 0
5759.12 0 0 0 −1.21685 + 1.87598i 0 0.176638 0 0 0
5759.13 0 0 0 0.555164 − 2.16605i 0 −1.93496 0 0 0
5759.14 0 0 0 0.555164 − 2.16605i 0 1.93496 0 0 0
5759.15 0 0 0 0.555164 + 2.16605i 0 −1.93496 0 0 0
5759.16 0 0 0 0.555164 + 2.16605i 0 1.93496 0 0 0
5759.17 0 0 0 0.784529 − 2.09392i 0 −4.20627 0 0 0
5759.18 0 0 0 0.784529 − 2.09392i 0 4.20627 0 0 0
5759.19 0 0 0 0.784529 + 2.09392i 0 −4.20627 0 0 0
5759.20 0 0 0 0.784529 + 2.09392i 0 4.20627 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5759.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
15.d odd 2 1 inner
60.h even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5760.2.o.b yes 24
3.b odd 2 1 5760.2.o.c yes 24
4.b odd 2 1 inner 5760.2.o.b yes 24
5.b even 2 1 5760.2.o.c yes 24
8.b even 2 1 5760.2.o.d yes 24
8.d odd 2 1 5760.2.o.d yes 24
12.b even 2 1 5760.2.o.c yes 24
15.d odd 2 1 inner 5760.2.o.b yes 24
20.d odd 2 1 5760.2.o.c yes 24
24.f even 2 1 5760.2.o.a ✓ 24
24.h odd 2 1 5760.2.o.a ✓ 24
40.e odd 2 1 5760.2.o.a ✓ 24
40.f even 2 1 5760.2.o.a ✓ 24
60.h even 2 1 inner 5760.2.o.b yes 24
120.i odd 2 1 5760.2.o.d yes 24
120.m even 2 1 5760.2.o.d yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5760.2.o.a ✓ 24 24.f even 2 1
5760.2.o.a ✓ 24 24.h odd 2 1
5760.2.o.a ✓ 24 40.e odd 2 1
5760.2.o.a ✓ 24 40.f even 2 1
5760.2.o.b yes 24 1.a even 1 1 trivial
5760.2.o.b yes 24 4.b odd 2 1 inner
5760.2.o.b yes 24 15.d odd 2 1 inner
5760.2.o.b yes 24 60.h even 2 1 inner
5760.2.o.c yes 24 3.b odd 2 1
5760.2.o.c yes 24 5.b even 2 1
5760.2.o.c yes 24 12.b even 2 1
5760.2.o.c yes 24 20.d odd 2 1
5760.2.o.d yes 24 8.b even 2 1
5760.2.o.d yes 24 8.d odd 2 1
5760.2.o.d yes 24 120.i odd 2 1
5760.2.o.d yes 24 120.m even 2 1