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Properties

Label 574.2.v.a
Level $574$
Weight $2$
Character orbit 574.v
Analytic conductor $4.583$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [574,2,Mod(3,574)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(574, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([4, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("574.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 574 = 2 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 574.v (of order \(24\), degree \(8\), 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: \(4.58341307602\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 112 q - 8 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 112 q - 8 q^{7} - 4 q^{9} + 8 q^{11} - 12 q^{12} + 4 q^{14} - 24 q^{15} + 56 q^{16} - 60 q^{17} + 56 q^{18} - 12 q^{19} + 32 q^{21} + 16 q^{22} - 12 q^{24} + 12 q^{26} - 4 q^{28} + 4 q^{30} - 108 q^{33} + 8 q^{35} + 8 q^{36} - 56 q^{37} - 40 q^{39} - 32 q^{42} - 4 q^{44} - 12 q^{46} + 36 q^{47} + 12 q^{49} - 64 q^{50} - 8 q^{51} - 4 q^{53} + 36 q^{54} + 4 q^{56} + 16 q^{57} - 24 q^{59} + 4 q^{60} + 36 q^{61} - 20 q^{63} - 20 q^{65} + 28 q^{67} - 20 q^{70} + 36 q^{73} - 96 q^{75} + 112 q^{77} + 80 q^{78} + 36 q^{79} - 12 q^{82} - 16 q^{84} - 16 q^{85} - 12 q^{87} - 4 q^{88} + 48 q^{89} + 108 q^{91} - 32 q^{92} + 56 q^{93} + 32 q^{95} - 32 q^{98} + 80 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3.1 0.965926 + 0.258819i −2.57525 + 1.97606i 0.866025 + 0.500000i −0.573464 − 0.153659i −2.99894 + 1.24220i −1.88240 − 1.85918i 0.707107 + 0.707107i 1.95064 − 7.27989i −0.514153 − 0.296847i
3.2 0.965926 + 0.258819i −2.54657 + 1.95405i 0.866025 + 0.500000i 2.06167 + 0.552422i −2.96555 + 1.22837i 2.59569 + 0.512219i 0.707107 + 0.707107i 1.89025 − 7.05450i 1.84844 + 1.06720i
3.3 0.965926 + 0.258819i −1.42399 + 1.09267i 0.866025 + 0.500000i 3.43739 + 0.921046i −1.65827 + 0.686879i −2.16416 + 1.52197i 0.707107 + 0.707107i 0.0573720 − 0.214115i 3.08188 + 1.77932i
3.4 0.965926 + 0.258819i −1.37072 + 1.05179i 0.866025 + 0.500000i −2.26132 − 0.605918i −1.59624 + 0.661184i 1.17598 + 2.37004i 0.707107 + 0.707107i −0.00384499 + 0.0143497i −2.02744 − 1.17054i
3.5 0.965926 + 0.258819i −1.34857 + 1.03480i 0.866025 + 0.500000i −0.0362543 − 0.00971430i −1.57045 + 0.650501i −1.19831 − 2.35883i 0.707107 + 0.707107i −0.0286097 + 0.106773i −0.0325047 − 0.0187666i
3.6 0.965926 + 0.258819i −1.09625 + 0.841181i 0.866025 + 0.500000i −3.70357 − 0.992369i −1.27661 + 0.528789i 0.479162 − 2.60200i 0.707107 + 0.707107i −0.282282 + 1.05349i −3.32053 − 1.91711i
3.7 0.965926 + 0.258819i −0.850000 + 0.652228i 0.866025 + 0.500000i 2.68641 + 0.719822i −0.989846 + 0.410008i 2.21468 − 1.44747i 0.707107 + 0.707107i −0.479358 + 1.78899i 2.40857 + 1.39059i
3.8 0.965926 + 0.258819i 0.253141 − 0.194242i 0.866025 + 0.500000i −0.697859 − 0.186991i 0.294789 − 0.122106i −1.49595 + 2.18223i 0.707107 + 0.707107i −0.750107 + 2.79944i −0.625683 − 0.361238i
3.9 0.965926 + 0.258819i 0.440466 − 0.337981i 0.866025 + 0.500000i −3.51660 − 0.942269i 0.512933 − 0.212464i −2.59558 + 0.512819i 0.707107 + 0.707107i −0.696678 + 2.60004i −3.15289 − 1.82032i
3.10 0.965926 + 0.258819i 0.552605 − 0.424029i 0.866025 + 0.500000i 1.31712 + 0.352922i 0.643522 − 0.266556i 1.54507 + 2.14773i 0.707107 + 0.707107i −0.650885 + 2.42914i 1.18090 + 0.681793i
3.11 0.965926 + 0.258819i 1.00401 − 0.770400i 0.866025 + 0.500000i 1.64374 + 0.440438i 1.16919 − 0.484294i 0.843933 − 2.50754i 0.707107 + 0.707107i −0.361947 + 1.35081i 1.47373 + 0.850860i
3.12 0.965926 + 0.258819i 1.98922 − 1.52638i 0.866025 + 0.500000i −2.24981 − 0.602834i 2.31650 − 0.959526i 2.20649 + 1.45994i 0.707107 + 0.707107i 0.850702 − 3.17486i −2.01712 − 1.16459i
3.13 0.965926 + 0.258819i 2.12432 − 1.63005i 0.866025 + 0.500000i 2.52164 + 0.675671i 2.47382 − 1.02469i −2.02214 + 1.70615i 0.707107 + 0.707107i 1.07922 − 4.02770i 2.26084 + 1.30530i
3.14 0.965926 + 0.258819i 2.30854 − 1.77140i 0.866025 + 0.500000i −0.629099 − 0.168566i 2.68835 − 1.11355i −1.12021 − 2.39690i 0.707107 + 0.707107i 1.41502 − 5.28093i −0.564034 − 0.325645i
243.1 0.258819 + 0.965926i −3.05633 + 0.402374i −0.866025 + 0.500000i 0.382104 + 1.42603i −1.17970 − 2.84805i 2.64559 + 0.0290266i −0.707107 − 0.707107i 6.28149 − 1.68312i −1.27854 + 0.738168i
243.2 0.258819 + 0.965926i −2.47072 + 0.325276i −0.866025 + 0.500000i 0.429867 + 1.60428i −0.953661 − 2.30234i −2.24626 − 1.39797i −0.707107 − 0.707107i 3.10086 − 0.830872i −1.43836 + 0.830439i
243.3 0.258819 + 0.965926i −2.18658 + 0.287869i −0.866025 + 0.500000i −1.06735 − 3.98340i −0.843989 − 2.03757i −2.49230 + 0.887955i −0.707107 − 0.707107i 1.80050 − 0.482442i 3.57142 − 2.06196i
243.4 0.258819 + 0.965926i −1.53216 + 0.201712i −0.866025 + 0.500000i −0.0495605 − 0.184962i −0.591390 − 1.42774i 1.65642 − 2.06307i −0.707107 − 0.707107i −0.590961 + 0.158348i 0.165833 − 0.0957436i
243.5 0.258819 + 0.965926i −0.873748 + 0.115031i −0.866025 + 0.500000i 0.998231 + 3.72545i −0.337254 − 0.814204i 1.29693 + 2.30607i −0.707107 − 0.707107i −2.14757 + 0.575441i −3.34015 + 1.92844i
243.6 0.258819 + 0.965926i −0.563941 + 0.0742443i −0.866025 + 0.500000i −0.174983 − 0.653047i −0.217673 − 0.525510i −2.01271 + 1.71727i −0.707107 − 0.707107i −2.58526 + 0.692718i 0.585506 − 0.338042i
See next 80 embeddings (of 112 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.d odd 6 1 inner
41.e odd 8 1 inner
287.w even 24 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 574.2.v.a ✓ 112
7.d odd 6 1 inner 574.2.v.a ✓ 112
41.e odd 8 1 inner 574.2.v.a ✓ 112
287.w even 24 1 inner 574.2.v.a ✓ 112
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.v.a ✓ 112 1.a even 1 1 trivial
574.2.v.a ✓ 112 7.d odd 6 1 inner
574.2.v.a ✓ 112 41.e odd 8 1 inner
574.2.v.a ✓ 112 287.w even 24 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{112} + 2 T_{3}^{110} + 2 T_{3}^{108} - 264 T_{3}^{107} + 132 T_{3}^{106} - 1044 T_{3}^{105} + \cdots + 63\!\cdots\!16 \) acting on \(S_{2}^{\mathrm{new}}(574, [\chi])\). Copy content Toggle raw display