Properties

Label 950.2.h.d
Level $950$
Weight $2$
Character orbit 950.h
Analytic conductor $7.586$
Analytic rank $0$
Dimension $44$
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] = [950,2,Mod(191,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.h (of order \(5\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
191.1 0.809017 + 0.587785i −1.00220 3.08444i 0.309017 + 0.951057i −2.22762 + 0.194172i 1.00220 3.08444i −1.89338 −0.309017 + 0.951057i −6.08232 + 4.41906i −1.91632 1.15227i
191.2 0.809017 + 0.587785i −0.806394 2.48183i 0.309017 + 0.951057i 1.11301 1.93938i 0.806394 2.48183i −1.68962 −0.309017 + 0.951057i −3.08213 + 2.23930i 2.04039 0.914782i
191.3 0.809017 + 0.587785i −0.734690 2.26114i 0.309017 + 0.951057i −0.796273 2.08949i 0.734690 2.26114i 3.12738 −0.309017 + 0.951057i −2.14595 + 1.55912i 0.583970 2.15847i
191.4 0.809017 + 0.587785i −0.320919 0.987687i 0.309017 + 0.951057i −0.846301 + 2.06973i 0.320919 0.987687i −2.76904 −0.309017 + 0.951057i 1.55451 1.12942i −1.90123 + 1.17700i
191.5 0.809017 + 0.587785i −0.183900 0.565985i 0.309017 + 0.951057i 2.14212 + 0.641332i 0.183900 0.565985i 2.23803 −0.309017 + 0.951057i 2.14053 1.55519i 1.35605 + 1.77796i
191.6 0.809017 + 0.587785i −0.00648263 0.0199515i 0.309017 + 0.951057i 2.20515 + 0.370553i 0.00648263 0.0199515i −4.68808 −0.309017 + 0.951057i 2.42669 1.76310i 1.56620 + 1.59594i
191.7 0.809017 + 0.587785i 0.0375929 + 0.115699i 0.309017 + 0.951057i −2.23367 + 0.103463i −0.0375929 + 0.115699i 1.64271 −0.309017 + 0.951057i 2.41508 1.75466i −1.86789 1.22922i
191.8 0.809017 + 0.587785i 0.154308 + 0.474912i 0.309017 + 0.951057i −1.19349 1.89092i −0.154308 + 0.474912i −2.61594 −0.309017 + 0.951057i 2.22532 1.61679i 0.145902 2.23130i
191.9 0.809017 + 0.587785i 0.578674 + 1.78097i 0.309017 + 0.951057i −1.13510 + 1.92654i −0.578674 + 1.78097i −2.72132 −0.309017 + 0.951057i −0.409956 + 0.297850i −2.05071 + 0.891406i
191.10 0.809017 + 0.587785i 0.611239 + 1.88120i 0.309017 + 0.951057i 2.16649 0.553476i −0.611239 + 1.88120i 2.35142 −0.309017 + 0.951057i −0.738252 + 0.536372i 2.07805 + 0.825657i
191.11 0.809017 + 0.587785i 0.863749 + 2.65835i 0.309017 + 0.951057i −1.38530 + 1.75527i −0.863749 + 2.65835i 3.39982 −0.309017 + 0.951057i −3.89370 + 2.82894i −2.15245 + 0.605783i
381.1 −0.309017 0.951057i −2.30507 + 1.67473i −0.809017 + 0.587785i −0.482704 2.18335i 2.30507 + 1.67473i −2.79249 0.809017 + 0.587785i 1.58157 4.86758i −1.92732 + 1.13377i
381.2 −0.309017 0.951057i −2.00675 + 1.45799i −0.809017 + 0.587785i −2.21649 + 0.295244i 2.00675 + 1.45799i 2.78117 0.809017 + 0.587785i 0.974256 2.99845i 0.965727 + 2.01677i
381.3 −0.309017 0.951057i −1.70816 + 1.24105i −0.809017 + 0.587785i 2.12953 0.681987i 1.70816 + 1.24105i −1.90564 0.809017 + 0.587785i 0.450556 1.38667i −1.30667 1.81456i
381.4 −0.309017 0.951057i −1.20914 + 0.878491i −0.809017 + 0.587785i 0.176849 2.22906i 1.20914 + 0.878491i 2.76699 0.809017 + 0.587785i −0.236780 + 0.728734i −2.17461 + 0.520625i
381.5 −0.309017 0.951057i −0.628367 + 0.456535i −0.809017 + 0.587785i −0.766450 + 2.10061i 0.628367 + 0.456535i −4.62972 0.809017 + 0.587785i −0.740631 + 2.27943i 2.23464 + 0.0798131i
381.6 −0.309017 0.951057i −0.591887 + 0.430031i −0.809017 + 0.587785i 1.69555 + 1.45777i 0.591887 + 0.430031i 1.38478 0.809017 + 0.587785i −0.761648 + 2.34411i 0.862467 2.06304i
381.7 −0.309017 0.951057i 0.616737 0.448085i −0.809017 + 0.587785i −1.35137 + 1.78152i −0.616737 0.448085i −0.0296482 0.809017 + 0.587785i −0.747467 + 2.30047i 2.11192 + 0.734710i
381.8 −0.309017 0.951057i 0.823288 0.598153i −0.809017 + 0.587785i −1.34910 1.78323i −0.823288 0.598153i 3.63885 0.809017 + 0.587785i −0.607036 + 1.86826i −1.27906 + 1.83412i
381.9 −0.309017 0.951057i 2.31854 1.68452i −0.809017 + 0.587785i 1.05411 1.97202i −2.31854 1.68452i −0.662081 0.809017 + 0.587785i 1.61098 4.95809i −2.20124 0.393129i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 191.11
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
25.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 950.2.h.d 44
25.d even 5 1 inner 950.2.h.d 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
950.2.h.d 44 1.a even 1 1 trivial
950.2.h.d 44 25.d even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{44} + T_{3}^{43} + 17 T_{3}^{42} + 7 T_{3}^{41} + 247 T_{3}^{40} + 398 T_{3}^{39} + 3568 T_{3}^{38} + 5780 T_{3}^{37} + 38850 T_{3}^{36} + 69157 T_{3}^{35} + 362221 T_{3}^{34} + 729119 T_{3}^{33} + 3190375 T_{3}^{32} + \cdots + 1936 \) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\). Copy content Toggle raw display