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Properties

Label 460.2.m.a
Level $460$
Weight $2$
Character orbit 460.m
Analytic conductor $3.673$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(41,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
41.1 0 −1.26886 + 1.46434i 0 −0.142315 + 0.989821i 0 0.0191296 + 0.0418879i 0 −0.107349 − 0.746632i 0
41.2 0 0.329283 − 0.380013i 0 −0.142315 + 0.989821i 0 −0.847137 − 1.85497i 0 0.390962 + 2.71920i 0
41.3 0 0.939578 − 1.08433i 0 −0.142315 + 0.989821i 0 2.04060 + 4.46829i 0 0.133978 + 0.931838i 0
81.1 0 −0.161849 + 1.12569i 0 −0.959493 + 0.281733i 0 0.847514 + 0.978083i 0 1.63751 + 0.480815i 0
81.2 0 −0.0800965 + 0.557084i 0 −0.959493 + 0.281733i 0 −2.98213 − 3.44157i 0 2.57455 + 0.755957i 0
81.3 0 0.241946 − 1.68277i 0 −0.959493 + 0.281733i 0 2.58157 + 2.97929i 0 0.105306 + 0.0309206i 0
101.1 0 −1.26886 − 1.46434i 0 −0.142315 − 0.989821i 0 0.0191296 − 0.0418879i 0 −0.107349 + 0.746632i 0
101.2 0 0.329283 + 0.380013i 0 −0.142315 − 0.989821i 0 −0.847137 + 1.85497i 0 0.390962 − 2.71920i 0
101.3 0 0.939578 + 1.08433i 0 −0.142315 − 0.989821i 0 2.04060 − 4.46829i 0 0.133978 − 0.931838i 0
121.1 0 −2.73464 − 0.802964i 0 0.841254 − 0.540641i 0 −0.359196 + 2.49826i 0 4.30976 + 2.76972i 0
121.2 0 0.0447663 + 0.0131446i 0 0.841254 − 0.540641i 0 0.423834 − 2.94783i 0 −2.52193 − 1.62075i 0
121.3 0 2.68988 + 0.789819i 0 0.841254 − 0.540641i 0 −0.0887134 + 0.617015i 0 4.08786 + 2.62711i 0
141.1 0 −1.08673 + 2.37960i 0 −0.654861 + 0.755750i 0 0.0544585 − 0.0349983i 0 −2.51694 − 2.90471i 0
141.2 0 0.256560 − 0.561788i 0 −0.654861 + 0.755750i 0 −1.01950 + 0.655191i 0 1.71480 + 1.97898i 0
141.3 0 0.830167 − 1.81781i 0 −0.654861 + 0.755750i 0 2.04574 − 1.31472i 0 −0.650684 − 0.750930i 0
261.1 0 −1.08673 − 2.37960i 0 −0.654861 − 0.755750i 0 0.0544585 + 0.0349983i 0 −2.51694 + 2.90471i 0
261.2 0 0.256560 + 0.561788i 0 −0.654861 − 0.755750i 0 −1.01950 − 0.655191i 0 1.71480 − 1.97898i 0
261.3 0 0.830167 + 1.81781i 0 −0.654861 − 0.755750i 0 2.04574 + 1.31472i 0 −0.650684 + 0.750930i 0
301.1 0 −0.161849 − 1.12569i 0 −0.959493 − 0.281733i 0 0.847514 − 0.978083i 0 1.63751 − 0.480815i 0
301.2 0 −0.0800965 − 0.557084i 0 −0.959493 − 0.281733i 0 −2.98213 + 3.44157i 0 2.57455 − 0.755957i 0
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 41.3
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 460.2.m.a ✓ 30
23.c even 11 1 inner 460.2.m.a ✓ 30
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
460.2.m.a ✓ 30 1.a even 1 1 trivial
460.2.m.a ✓ 30 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{30} - 6 T_{3}^{28} - 7 T_{3}^{27} + 25 T_{3}^{26} + 73 T_{3}^{25} + 31 T_{3}^{24} - 349 T_{3}^{23} + \cdots + 1 \) acting on \(S_{2}^{\mathrm{new}}(460, [\chi])\). Copy content Toggle raw display