↑

Properties

Label 4025.2.a.bd
Level $4025$
Weight $2$
Character orbit 4025.a
Self dual yes
Analytic conductor $32.140$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4025,2,Mod(1,4025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4025.a (trivial)

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: yes
Analytic conductor: \(32.1397868136\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 805)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.72900 3.06108 5.44746 0 −8.35371 −1.00000 −9.40815 6.37023 0
1.2 −2.70441 −1.97894 5.31383 0 5.35185 −1.00000 −8.96197 0.916187 0
1.3 −2.57149 −0.285863 4.61257 0 0.735095 −1.00000 −6.71821 −2.91828 0
1.4 −2.35921 −2.50751 3.56589 0 5.91575 −1.00000 −3.69426 3.28760 0
1.5 −2.11197 1.59044 2.46043 0 −3.35897 −1.00000 −0.972410 −0.470497 0
1.6 −1.61751 2.88096 0.616354 0 −4.65999 −1.00000 2.23807 5.29992 0
1.7 −1.50084 0.816695 0.252529 0 −1.22573 −1.00000 2.62268 −2.33301 0
1.8 −1.30923 −2.43985 −0.285909 0 3.19433 −1.00000 2.99279 2.95286 0
1.9 −0.817573 −1.89500 −1.33157 0 1.54930 −1.00000 2.72381 0.591014 0
1.10 −0.475047 0.568069 −1.77433 0 −0.269859 −1.00000 1.79298 −2.67730 0
1.11 0.157646 −0.829461 −1.97515 0 −0.130761 −1.00000 −0.626665 −2.31200 0
1.12 0.294301 −3.07644 −1.91339 0 −0.905400 −1.00000 −1.15171 6.46449 0
1.13 0.556064 2.94180 −1.69079 0 1.63583 −1.00000 −2.05232 5.65418 0
1.14 0.685218 1.12744 −1.53048 0 0.772540 −1.00000 −2.41915 −1.72889 0
1.15 1.22234 −1.28664 −0.505878 0 −1.57271 −1.00000 −3.06304 −1.34457 0
1.16 1.53505 0.943091 0.356385 0 1.44769 −1.00000 −2.52303 −2.11058 0
1.17 1.67541 −3.24787 0.806990 0 −5.44150 −1.00000 −1.99878 7.54864 0
1.18 2.20248 2.83822 2.85093 0 6.25112 −1.00000 1.87416 5.05547 0
1.19 2.38755 −1.09554 3.70041 0 −2.61567 −1.00000 4.05982 −1.79978 0
1.20 2.68001 3.08395 5.18247 0 8.26504 −1.00000 8.52906 6.51078 0
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(1\)
\(23\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4025.2.a.bd 21
5.b even 2 1 4025.2.a.be 21
5.c odd 4 2 805.2.c.c ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.c.c ✓ 42 5.c odd 4 2
4025.2.a.bd 21 1.a even 1 1 trivial
4025.2.a.be 21 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\):

\( T_{2}^{21} + 2 T_{2}^{20} - 34 T_{2}^{19} - 66 T_{2}^{18} + 485 T_{2}^{17} + 904 T_{2}^{16} - 3786 T_{2}^{15} + \cdots - 256 \) Copy content Toggle raw display
\( T_{3}^{21} - T_{3}^{20} - 46 T_{3}^{19} + 38 T_{3}^{18} + 890 T_{3}^{17} - 570 T_{3}^{16} - 9413 T_{3}^{15} + \cdots + 2848 \) Copy content Toggle raw display
\( T_{11}^{21} - 7 T_{11}^{20} - 121 T_{11}^{19} + 953 T_{11}^{18} + 5502 T_{11}^{17} - 53080 T_{11}^{16} + \cdots + 73032192 \) Copy content Toggle raw display