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Properties

Label 574.2.u.b
Level $574$
Weight $2$
Character orbit 574.u
Analytic conductor $4.583$
Analytic rank $0$
Dimension $96$
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] = [574,2,Mod(43,574)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(574, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("574.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 574 = 2 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 574.u (of order \(20\), 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: \(96\)
Relative dimension: \(12\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q + 24 q^{4} + 4 q^{11} + 12 q^{13} + 28 q^{15} - 24 q^{16} - 8 q^{17} - 32 q^{18} + 4 q^{19} + 20 q^{20} + 4 q^{22} + 32 q^{23} + 48 q^{25} - 8 q^{26} - 12 q^{29} - 28 q^{30} - 28 q^{31} + 8 q^{34} + 8 q^{35} - 4 q^{37} - 4 q^{38} - 80 q^{39} - 24 q^{41} + 32 q^{42} - 4 q^{44} + 12 q^{45} - 20 q^{46} + 24 q^{47} + 12 q^{51} + 8 q^{52} + 16 q^{53} + 36 q^{55} - 52 q^{57} - 12 q^{58} + 12 q^{59} - 8 q^{60} - 100 q^{61} + 24 q^{64} + 12 q^{65} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 168 q^{69} - 8 q^{70} - 44 q^{71} + 32 q^{72} - 20 q^{74} + 64 q^{75} + 16 q^{76} - 40 q^{77} + 88 q^{78} + 48 q^{79} + 20 q^{80} - 256 q^{81} + 24 q^{82} + 8 q^{83} - 152 q^{85} + 28 q^{86} - 60 q^{87} - 4 q^{88} + 44 q^{89} + 8 q^{92} - 4 q^{94} + 68 q^{95} + 64 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
43.1 −0.951057 + 0.309017i −2.21915 + 2.21915i 0.809017 − 0.587785i 0.305276 + 0.420176i 1.42478 − 2.79629i 0.453990 + 0.891007i −0.587785 + 0.809017i − 6.84927i −0.420176 − 0.305276i
43.2 −0.951057 + 0.309017i −2.02089 + 2.02089i 0.809017 − 0.587785i 1.13531 + 1.56261i 1.29749 − 2.54647i −0.453990 − 0.891007i −0.587785 + 0.809017i − 5.16800i −1.56261 − 1.13531i
43.3 −0.951057 + 0.309017i −1.39795 + 1.39795i 0.809017 − 0.587785i −1.26267 − 1.73792i 0.897539 − 1.76152i 0.453990 + 0.891007i −0.587785 + 0.809017i − 0.908531i 1.73792 + 1.26267i
43.4 −0.951057 + 0.309017i −0.703392 + 0.703392i 0.809017 − 0.587785i 1.76548 + 2.42998i 0.451606 − 0.886326i 0.453990 + 0.891007i −0.587785 + 0.809017i 2.01048i −2.42998 − 1.76548i
43.5 −0.951057 + 0.309017i −0.690380 + 0.690380i 0.809017 − 0.587785i −0.814326 − 1.12082i 0.443251 − 0.869930i −0.453990 − 0.891007i −0.587785 + 0.809017i 2.04675i 1.12082 + 0.814326i
43.6 −0.951057 + 0.309017i −0.605449 + 0.605449i 0.809017 − 0.587785i −1.78104 − 2.45139i 0.388722 − 0.762910i 0.453990 + 0.891007i −0.587785 + 0.809017i 2.26686i 2.45139 + 1.78104i
43.7 −0.951057 + 0.309017i −0.122638 + 0.122638i 0.809017 − 0.587785i 1.37210 + 1.88854i 0.0787381 − 0.154532i −0.453990 − 0.891007i −0.587785 + 0.809017i 2.96992i −1.88854 − 1.37210i
43.8 −0.951057 + 0.309017i 0.744075 − 0.744075i 0.809017 − 0.587785i −1.01864 − 1.40204i −0.477726 + 0.937589i −0.453990 − 0.891007i −0.587785 + 0.809017i 1.89270i 1.40204 + 1.01864i
43.9 −0.951057 + 0.309017i 1.11527 − 1.11527i 0.809017 − 0.587785i 0.910558 + 1.25328i −0.716046 + 1.40532i 0.453990 + 0.891007i −0.587785 + 0.809017i 0.512358i −1.25328 − 0.910558i
43.10 −0.951057 + 0.309017i 1.70498 − 1.70498i 0.809017 − 0.587785i −0.178553 − 0.245757i −1.09466 + 2.14840i −0.453990 − 0.891007i −0.587785 + 0.809017i − 2.81390i 0.245757 + 0.178553i
43.11 −0.951057 + 0.309017i 1.79907 − 1.79907i 0.809017 − 0.587785i 2.50084 + 3.44211i −1.15507 + 2.26696i −0.453990 − 0.891007i −0.587785 + 0.809017i − 3.47331i −3.44211 − 2.50084i
43.12 −0.951057 + 0.309017i 2.39646 − 2.39646i 0.809017 − 0.587785i −0.698261 − 0.961074i −1.53862 + 3.01972i 0.453990 + 0.891007i −0.587785 + 0.809017i − 8.48607i 0.961074 + 0.698261i
169.1 0.587785 + 0.809017i −2.01293 − 2.01293i −0.309017 + 0.951057i −4.05120 − 1.31631i 0.445324 − 2.81166i −0.156434 − 0.987688i −0.951057 + 0.309017i 5.10377i −1.31631 − 4.05120i
169.2 0.587785 + 0.809017i −1.90030 − 1.90030i −0.309017 + 0.951057i −0.308976 − 0.100392i 0.420407 − 2.65434i 0.156434 + 0.987688i −0.951057 + 0.309017i 4.22228i −0.100392 − 0.308976i
169.3 0.587785 + 0.809017i −1.67350 − 1.67350i −0.309017 + 0.951057i 3.38304 + 1.09922i 0.370230 − 2.33754i 0.156434 + 0.987688i −0.951057 + 0.309017i 2.60117i 1.09922 + 3.38304i
169.4 0.587785 + 0.809017i −0.976863 − 0.976863i −0.309017 + 0.951057i 0.298391 + 0.0969530i 0.216113 − 1.36448i −0.156434 − 0.987688i −0.951057 + 0.309017i − 1.09148i 0.0969530 + 0.298391i
169.5 0.587785 + 0.809017i −0.695930 − 0.695930i −0.309017 + 0.951057i −1.99371 − 0.647795i 0.153962 − 0.972076i 0.156434 + 0.987688i −0.951057 + 0.309017i − 2.03136i −0.647795 − 1.99371i
169.6 0.587785 + 0.809017i −0.409436 − 0.409436i −0.309017 + 0.951057i −1.78146 − 0.578833i 0.0905803 − 0.571901i 0.156434 + 0.987688i −0.951057 + 0.309017i − 2.66472i −0.578833 − 1.78146i
169.7 0.587785 + 0.809017i −0.174745 − 0.174745i −0.309017 + 0.951057i 3.01809 + 0.980636i 0.0386592 − 0.244085i −0.156434 − 0.987688i −0.951057 + 0.309017i − 2.93893i 0.980636 + 3.01809i
169.8 0.587785 + 0.809017i 0.725112 + 0.725112i −0.309017 + 0.951057i −3.96108 − 1.28703i −0.160418 + 1.01284i −0.156434 − 0.987688i −0.951057 + 0.309017i − 1.94843i −1.28703 − 3.96108i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 43.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
41.g even 20 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 574.2.u.b ✓ 96
41.g even 20 1 inner 574.2.u.b ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.u.b ✓ 96 1.a even 1 1 trivial
574.2.u.b ✓ 96 41.g even 20 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{96} + 784 T_{3}^{92} + 20 T_{3}^{91} - 408 T_{3}^{89} + 275130 T_{3}^{88} + 9856 T_{3}^{87} + \cdots + 10926885581056 \) acting on \(S_{2}^{\mathrm{new}}(574, [\chi])\). Copy content Toggle raw display