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Properties

Label 275.2.y.b
Level $275$
Weight $2$
Character orbit 275.y
Analytic conductor $2.196$
Analytic rank $0$
Dimension $56$
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] = [275,2,Mod(34,275)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(275, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("275.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.y (of order \(10\), degree \(4\), 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: \(2.19588605559\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 16 q^{4} - 7 q^{5} - 4 q^{6} - 15 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 56 q + 16 q^{4} - 7 q^{5} - 4 q^{6} - 15 q^{8} + 10 q^{9} + 10 q^{10} + 14 q^{11} - 20 q^{12} - 6 q^{14} - 21 q^{15} - 20 q^{16} + 20 q^{17} + 10 q^{19} + 22 q^{20} - 6 q^{21} + 10 q^{23} - 62 q^{24} + 9 q^{25} - 4 q^{26} + 18 q^{29} - 129 q^{30} - 16 q^{34} + 42 q^{35} - 26 q^{36} - 65 q^{37} - 20 q^{38} + 20 q^{39} - 28 q^{40} - 10 q^{41} + 60 q^{42} - 16 q^{44} - 18 q^{45} + 6 q^{46} - 25 q^{47} + 15 q^{48} - 104 q^{49} + 98 q^{50} + 54 q^{51} + 90 q^{52} + 5 q^{53} + 55 q^{54} - 3 q^{55} + 10 q^{56} - 10 q^{58} + 34 q^{59} + 133 q^{60} - 20 q^{61} - 10 q^{62} + 20 q^{63} + 25 q^{64} - 10 q^{65} + 4 q^{66} - 15 q^{67} - 2 q^{69} - 4 q^{70} - 13 q^{71} - 5 q^{72} - 70 q^{73} - 30 q^{74} - 80 q^{75} + 140 q^{76} - 65 q^{78} + 15 q^{79} - 131 q^{80} - 99 q^{81} + 60 q^{83} + 76 q^{84} + 43 q^{85} + 43 q^{86} - 175 q^{87} + 30 q^{88} + 27 q^{89} + 73 q^{90} - 10 q^{91} - 80 q^{92} - 17 q^{94} + 18 q^{95} - 148 q^{96} - 15 q^{97} - 80 q^{98} + 70 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
34.1 −1.57412 + 2.16659i 2.31407 − 0.751886i −1.59823 − 4.91884i −0.365105 + 2.20606i −2.01359 + 6.19720i 0.484947i 8.07896 + 2.62501i 2.36252 − 1.71647i −4.20491 − 4.26364i
34.2 −1.43956 + 1.98138i −2.90582 + 0.944157i −1.23550 − 3.80249i 0.822716 − 2.07922i 2.31235 − 7.11669i 1.65047i 4.65425 + 1.51226i 5.12529 − 3.72374i 2.93537 + 4.62326i
34.3 −1.27151 + 1.75008i 0.651279 − 0.211613i −0.828011 − 2.54836i −2.07156 − 0.841819i −0.457765 + 1.40886i 0.204568i 1.39796 + 0.454225i −2.04767 + 1.48772i 4.10724 − 2.55500i
34.4 −0.837356 + 1.15252i 0.390909 − 0.127014i −0.00910732 − 0.0280294i 0.370423 − 2.20517i −0.180944 + 0.556887i 3.40752i −2.66981 − 0.867474i −2.29037 + 1.66405i 2.23133 + 2.27344i
34.5 −0.793392 + 1.09201i −2.53067 + 0.822263i 0.0550186 + 0.169330i −2.19253 + 0.439083i 1.10989 − 3.41589i − 3.91598i −2.79603 − 0.908485i 3.30110 − 2.39839i 1.26006 − 2.74263i
34.6 −0.186979 + 0.257354i −1.68203 + 0.546526i 0.586764 + 1.80587i 0.438872 + 2.19258i 0.173854 − 0.535068i − 0.334460i −1.17954 − 0.383255i 0.103500 − 0.0751969i −0.646328 − 0.297020i
34.7 −0.178512 + 0.245700i 1.82141 − 0.591813i 0.589532 + 1.81439i 2.06158 − 0.865969i −0.179735 + 0.553167i − 3.28003i −1.12871 − 0.366740i 0.540253 − 0.392517i −0.155247 + 0.661115i
34.8 −0.147001 + 0.202329i 2.78106 − 0.903620i 0.598706 + 1.84263i −1.73840 + 1.40640i −0.225989 + 0.695521i 0.383179i −0.936531 − 0.304297i 4.49070 − 3.26268i −0.0290105 − 0.558471i
34.9 0.586088 − 0.806680i −0.165471 + 0.0537647i 0.310799 + 0.956542i 2.03580 − 0.924950i −0.0536094 + 0.164993i 4.19664i 2.85040 + 0.926151i −2.40256 + 1.74556i 0.447016 − 2.18434i
34.10 0.848821 − 1.16830i 1.36117 − 0.442272i −0.0263979 − 0.0812445i −2.04831 − 0.896892i 0.638686 − 1.96567i − 4.85801i 2.62952 + 0.854382i −0.769861 + 0.559337i −2.78649 + 1.63175i
34.11 0.850736 − 1.17094i −1.05824 + 0.343843i −0.0293094 − 0.0902052i −1.61420 + 1.54738i −0.497664 + 1.53165i 1.92880i 2.62248 + 0.852096i −1.42541 + 1.03562i 0.438625 + 3.20653i
34.12 1.13691 − 1.56482i −2.79913 + 0.909493i −0.538063 − 1.65599i 2.04143 + 0.912454i −1.75916 + 5.41414i − 4.49516i 0.476063 + 0.154682i 4.58091 − 3.32823i 3.74874 − 2.15709i
34.13 1.40881 − 1.93906i 2.16543 − 0.703590i −1.15717 − 3.56140i −1.75916 − 1.38035i 1.68637 − 5.19011i 4.20978i −3.97699 − 1.29220i 1.76699 − 1.28379i −5.15489 + 1.46647i
34.14 1.59706 − 2.19817i 0.774067 − 0.251509i −1.66330 − 5.11912i 1.70943 + 1.44147i 0.683373 − 2.10321i 0.417733i −8.74087 − 2.84008i −1.89113 + 1.37399i 5.89867 − 1.45551i
89.1 −1.57412 − 2.16659i 2.31407 + 0.751886i −1.59823 + 4.91884i −0.365105 − 2.20606i −2.01359 − 6.19720i − 0.484947i 8.07896 − 2.62501i 2.36252 + 1.71647i −4.20491 + 4.26364i
89.2 −1.43956 − 1.98138i −2.90582 − 0.944157i −1.23550 + 3.80249i 0.822716 + 2.07922i 2.31235 + 7.11669i − 1.65047i 4.65425 − 1.51226i 5.12529 + 3.72374i 2.93537 − 4.62326i
89.3 −1.27151 − 1.75008i 0.651279 + 0.211613i −0.828011 + 2.54836i −2.07156 + 0.841819i −0.457765 − 1.40886i − 0.204568i 1.39796 − 0.454225i −2.04767 − 1.48772i 4.10724 + 2.55500i
89.4 −0.837356 − 1.15252i 0.390909 + 0.127014i −0.00910732 + 0.0280294i 0.370423 + 2.20517i −0.180944 − 0.556887i − 3.40752i −2.66981 + 0.867474i −2.29037 − 1.66405i 2.23133 − 2.27344i
89.5 −0.793392 − 1.09201i −2.53067 − 0.822263i 0.0550186 − 0.169330i −2.19253 − 0.439083i 1.10989 + 3.41589i 3.91598i −2.79603 + 0.908485i 3.30110 + 2.39839i 1.26006 + 2.74263i
89.6 −0.186979 − 0.257354i −1.68203 − 0.546526i 0.586764 − 1.80587i 0.438872 − 2.19258i 0.173854 + 0.535068i 0.334460i −1.17954 + 0.383255i 0.103500 + 0.0751969i −0.646328 + 0.297020i
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 34.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
25.e even 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 275.2.y.b ✓ 56
25.e even 10 1 inner 275.2.y.b ✓ 56
25.f odd 20 2 6875.2.a.n 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
275.2.y.b ✓ 56 1.a even 1 1 trivial
275.2.y.b ✓ 56 25.e even 10 1 inner
6875.2.a.n 56 25.f odd 20 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{56} - 22 T_{2}^{54} + 5 T_{2}^{53} + 299 T_{2}^{52} - 110 T_{2}^{51} - 3243 T_{2}^{50} + \cdots + 614656 \) acting on \(S_{2}^{\mathrm{new}}(275, [\chi])\). Copy content Toggle raw display