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Properties

Label 6025.2.a.n
Level $6025$
Weight $2$
Character orbit 6025.a
Self dual yes
Analytic conductor $48.110$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.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: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 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 −2.56980 0.961984 4.60385 0 −2.47210 2.40958 −6.69138 −2.07459 0
1.2 −2.49215 0.300645 4.21080 0 −0.749251 2.12232 −5.50965 −2.90961 0
1.3 −2.35802 2.46294 3.56028 0 −5.80768 −4.19376 −3.67917 3.06609 0
1.4 −2.31444 −1.11942 3.35665 0 2.59084 1.28338 −3.13990 −1.74690 0
1.5 −2.11193 3.26338 2.46023 0 −6.89202 1.21893 −0.971967 7.64967 0
1.6 −1.94004 1.97205 1.76376 0 −3.82586 −2.17744 0.458324 0.888995 0
1.7 −1.93842 −1.97315 1.75746 0 3.82479 −0.0385515 0.470139 0.893333 0
1.8 −1.82970 −1.30801 1.34779 0 2.39326 2.38020 1.19335 −1.28911 0
1.9 −1.70335 −3.34921 0.901404 0 5.70487 4.14952 1.87129 8.21718 0
1.10 −1.43348 2.46422 0.0548683 0 −3.53241 5.17959 2.78831 3.07238 0
1.11 −1.35529 0.00323419 −0.163197 0 −0.00438325 −1.75164 2.93175 −2.99999 0
1.12 −1.11018 −0.936293 −0.767491 0 1.03946 −2.02452 3.07242 −2.12335 0
1.13 −0.785880 −0.0947217 −1.38239 0 0.0744399 3.94418 2.65816 −2.99103 0
1.14 −0.628757 −2.03617 −1.60466 0 1.28026 0.952044 2.26646 1.14599 0
1.15 −0.460717 3.13691 −1.78774 0 −1.44523 1.56377 1.74508 6.84020 0
1.16 −0.409457 −1.91892 −1.83235 0 0.785714 −3.66070 1.56918 0.682248 0
1.17 −0.337207 −2.44634 −1.88629 0 0.824921 −2.26789 1.31048 2.98457 0
1.18 −0.230402 1.04564 −1.94691 0 −0.240918 1.53080 0.909377 −1.90664 0
1.19 −0.0794983 0.864949 −1.99368 0 −0.0687619 −0.264036 0.317491 −2.25186 0
1.20 0.221853 −0.516508 −1.95078 0 −0.114589 −0.263042 −0.876492 −2.73322 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.40
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(241\) \(-1\)

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 6025.2.a.n yes 40
5.b even 2 1 6025.2.a.m ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6025.2.a.m ✓ 40 5.b even 2 1
6025.2.a.n yes 40 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

\( T_{2}^{40} - 9 T_{2}^{39} - 20 T_{2}^{38} + 402 T_{2}^{37} - 310 T_{2}^{36} - 7915 T_{2}^{35} + \cdots - 1125 \) Copy content Toggle raw display
\( T_{3}^{40} - 8 T_{3}^{39} - 47 T_{3}^{38} + 522 T_{3}^{37} + 684 T_{3}^{36} - 15275 T_{3}^{35} + \cdots + 5329 \) Copy content Toggle raw display