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Properties

Label 950.2.h.c
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + 3 q^{14} - 4 q^{15} - 11 q^{16} + 11 q^{17} + 42 q^{18} + 11 q^{19} - 6 q^{20} + 3 q^{21} - 6 q^{22} - 3 q^{23} + 6 q^{24} - 11 q^{25} + 22 q^{26} - 23 q^{27} - 12 q^{28} + 36 q^{29} - 4 q^{30} + 11 q^{31} + 44 q^{32} + 2 q^{33} - 19 q^{34} + 67 q^{35} - 8 q^{36} + 3 q^{37} + 11 q^{38} + 47 q^{39} + 4 q^{40} + 2 q^{41} + 3 q^{42} + 70 q^{43} - 6 q^{44} - 28 q^{45} - 8 q^{46} - 11 q^{47} - 4 q^{48} + 22 q^{49} + 14 q^{50} + 38 q^{51} + 2 q^{52} - 9 q^{53} + 32 q^{54} + 8 q^{55} - 12 q^{56} - 6 q^{57} + 36 q^{58} - 62 q^{59} + 11 q^{60} - 28 q^{61} - 29 q^{62} + 10 q^{63} - 11 q^{64} - 39 q^{65} - 8 q^{66} + 25 q^{67} + 16 q^{68} - 81 q^{69} - 43 q^{70} - 34 q^{71} - 13 q^{72} + 6 q^{73} + 8 q^{74} - 39 q^{75} - 44 q^{76} - 21 q^{77} - 58 q^{78} + 19 q^{79} - q^{80} - 22 q^{81} + 2 q^{82} - 50 q^{83} - 7 q^{84} + 102 q^{85} - 10 q^{86} + 47 q^{87} - q^{88} - 4 q^{89} - 38 q^{90} - 8 q^{91} - 8 q^{92} + 60 q^{93} - 11 q^{94} - 4 q^{95} + q^{96} + 8 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
191.1 −0.809017 − 0.587785i −0.924522 − 2.84539i 0.309017 + 0.951057i 2.23604 + 0.0110743i −0.924522 + 2.84539i 2.08675 0.309017 − 0.951057i −4.81444 + 3.49789i −1.80249 − 1.32327i
191.2 −0.809017 − 0.587785i −0.636317 − 1.95838i 0.309017 + 0.951057i 0.252836 + 2.22173i −0.636317 + 1.95838i −0.354998 0.309017 − 0.951057i −1.00331 + 0.728944i 1.10135 − 1.94603i
191.3 −0.809017 − 0.587785i −0.474004 − 1.45883i 0.309017 + 0.951057i −1.96596 + 1.06536i −0.474004 + 1.45883i −4.21471 0.309017 − 0.951057i 0.523533 − 0.380369i 2.21670 + 0.293674i
191.4 −0.809017 − 0.587785i −0.351062 − 1.08046i 0.309017 + 0.951057i −0.646677 − 2.14052i −0.351062 + 1.08046i −1.02053 0.309017 − 0.951057i 1.38291 − 1.00474i −0.734991 + 2.11182i
191.5 −0.809017 − 0.587785i −0.207743 − 0.639367i 0.309017 + 0.951057i 2.21783 − 0.285024i −0.207743 + 0.639367i 0.622457 0.309017 − 0.951057i 2.06142 − 1.49771i −1.96179 − 1.07302i
191.6 −0.809017 − 0.587785i 0.142630 + 0.438971i 0.309017 + 0.951057i −2.07094 + 0.843327i 0.142630 − 0.438971i 3.64236 0.309017 − 0.951057i 2.25470 − 1.63813i 2.17112 + 0.535003i
191.7 −0.809017 − 0.587785i 0.429059 + 1.32051i 0.309017 + 0.951057i −1.05485 − 1.97162i 0.429059 − 1.32051i −3.34366 0.309017 − 0.951057i 0.867401 − 0.630204i −0.305496 + 2.21510i
191.8 −0.809017 − 0.587785i 0.445121 + 1.36994i 0.309017 + 0.951057i −0.223480 + 2.22487i 0.445121 − 1.36994i −0.156892 0.309017 − 0.951057i 0.748443 − 0.543776i 1.48855 − 1.66860i
191.9 −0.809017 − 0.587785i 0.549973 + 1.69264i 0.309017 + 0.951057i 1.41010 − 1.73540i 0.549973 − 1.69264i 4.16162 0.309017 − 0.951057i −0.135515 + 0.0984577i −2.16084 + 0.575134i
191.10 −0.809017 − 0.587785i 0.862591 + 2.65478i 0.309017 + 0.951057i 1.23726 + 1.86257i 0.862591 − 2.65478i 2.25004 0.309017 − 0.951057i −3.87675 + 2.81662i 0.0938288 − 2.23410i
191.11 −0.809017 − 0.587785i 0.973291 + 2.99548i 0.309017 + 0.951057i −2.20117 + 0.393528i 0.973291 − 2.99548i −2.52654 0.309017 − 0.951057i −5.59856 + 4.06759i 2.01209 + 0.975442i
381.1 0.309017 + 0.951057i −2.41843 + 1.75709i −0.809017 + 0.587785i −0.597004 − 2.15490i −2.41843 − 1.75709i 1.43148 −0.809017 − 0.587785i 1.83438 − 5.64563i 1.86495 − 1.23368i
381.2 0.309017 + 0.951057i −1.83642 + 1.33424i −0.809017 + 0.587785i −1.65745 + 1.50096i −1.83642 − 1.33424i 4.52091 −0.809017 − 0.587785i 0.665206 − 2.04729i −1.93967 − 1.11250i
381.3 0.309017 + 0.951057i −1.61479 + 1.17321i −0.809017 + 0.587785i 1.68004 + 1.47562i −1.61479 − 1.17321i 0.288481 −0.809017 − 0.587785i 0.304065 − 0.935817i −0.884238 + 2.05381i
381.4 0.309017 + 0.951057i −1.31294 + 0.953908i −0.809017 + 0.587785i −2.03947 + 0.916822i −1.31294 − 0.953908i −4.02398 −0.809017 − 0.587785i −0.113176 + 0.348320i −1.50218 − 1.65634i
381.5 0.309017 + 0.951057i −0.346707 + 0.251897i −0.809017 + 0.587785i 2.01954 − 0.959919i −0.346707 − 0.251897i −2.51273 −0.809017 − 0.587785i −0.870298 + 2.67850i 1.53701 + 1.62407i
381.6 0.309017 + 0.951057i −0.334955 + 0.243359i −0.809017 + 0.587785i 1.00269 + 1.99865i −0.334955 − 0.243359i 2.56738 −0.809017 − 0.587785i −0.874080 + 2.69014i −1.59098 + 1.57124i
381.7 0.309017 + 0.951057i 0.380239 − 0.276260i −0.809017 + 0.587785i 1.10489 − 1.94402i 0.380239 + 0.276260i 4.66404 −0.809017 − 0.587785i −0.858789 + 2.64308i 2.19030 + 0.450073i
381.8 0.309017 + 0.951057i 0.521494 − 0.378888i −0.809017 + 0.587785i −0.491086 − 2.18148i 0.521494 + 0.378888i −2.52980 −0.809017 − 0.587785i −0.798651 + 2.45799i 1.92295 − 1.14116i
381.9 0.309017 + 0.951057i 1.89683 − 1.37812i −0.809017 + 0.587785i 1.73578 − 1.40963i 1.89683 + 1.37812i 2.10540 −0.809017 − 0.587785i 0.771670 − 2.37496i 1.87702 + 1.21523i
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.c ✓ 44
25.d even 5 1 inner 950.2.h.c ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
950.2.h.c ✓ 44 1.a even 1 1 trivial
950.2.h.c ✓ 44 25.d even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{44} - T_{3}^{43} + 21 T_{3}^{42} - 5 T_{3}^{41} + 289 T_{3}^{40} + 24 T_{3}^{39} + 3566 T_{3}^{38} + \cdots + 6130576 \) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\). Copy content Toggle raw display