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Properties

Label 6025.2.a.m
Level $6025$
Weight $2$
Character orbit 6025.a
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
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: \(1\)
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 −2.80490 0.485560 5.86748 0 −1.36195 4.89210 −10.8479 −2.76423 0
1.2 −2.72336 −1.81872 5.41670 0 4.95303 −1.94325 −9.30491 0.307738 0
1.3 −2.67715 1.88460 5.16713 0 −5.04535 −1.59154 −8.47889 0.551710 0
1.4 −2.61751 −2.91594 4.85138 0 7.63252 2.00988 −7.46353 5.50273 0
1.5 −2.47202 −1.05364 4.11086 0 2.60461 −3.75256 −5.21808 −1.88985 0
1.6 −2.30867 −1.94403 3.32995 0 4.48812 −0.292911 −3.07041 0.779258 0
1.7 −2.16066 −3.21615 2.66843 0 6.94900 −3.61887 −1.44426 7.34365 0
1.8 −2.15543 0.792453 2.64590 0 −1.70808 −4.02126 −1.39219 −2.37202 0
1.9 −2.14986 1.70160 2.62188 0 −3.65820 3.86024 −1.33695 −0.104549 0
1.10 −1.98624 2.93351 1.94516 0 −5.82666 −3.87755 0.108919 5.60547 0
1.11 −1.73371 −1.68845 1.00575 0 2.92728 1.46765 1.72373 −0.149147 0
1.12 −1.58708 1.81144 0.518823 0 −2.87490 0.0644914 2.35075 0.281309 0
1.13 −1.58658 2.51389 0.517252 0 −3.98850 −3.57092 2.35251 3.31964 0
1.14 −1.41467 −0.773938 0.00129837 0 1.09487 2.74877 2.82751 −2.40102 0
1.15 −1.00174 2.95041 −0.996521 0 −2.95554 −1.49397 3.00173 5.70493 0
1.16 −0.863616 −1.78313 −1.25417 0 1.53994 −4.46828 2.81035 0.179539 0
1.17 −0.833391 −0.371715 −1.30546 0 0.309784 3.36045 2.75474 −2.86183 0
1.18 −0.811989 −3.20147 −1.34067 0 2.59956 1.14623 2.71259 7.24939 0
1.19 −0.645204 −2.49795 −1.58371 0 1.61169 −3.74088 2.31222 3.23976 0
1.20 −0.333070 −1.03111 −1.88906 0 0.343432 2.91492 1.29533 −1.93681 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.m ✓ 40
5.b even 2 1 6025.2.a.n yes 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6025.2.a.m ✓ 40 1.a even 1 1 trivial
6025.2.a.n yes 40 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

\( T_{2}^{40} + 9 T_{2}^{39} - 20 T_{2}^{38} - 402 T_{2}^{37} - 310 T_{2}^{36} + 7915 T_{2}^{35} + \cdots - 1125 \) 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