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Properties

Label 595.2.c.b
Level $595$
Weight $2$
Character orbit 595.c
Analytic conductor $4.751$
Analytic rank $0$
Dimension $34$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [595,2,Mod(239,595)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(595, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("595.239");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 595 = 5 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 595.c (of order \(2\), degree \(1\), 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: \(4.75109892027\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 44 q^{4} + 2 q^{5} + 12 q^{6} - 58 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 34 q - 44 q^{4} + 2 q^{5} + 12 q^{6} - 58 q^{9} - 8 q^{10} + 20 q^{11} - 4 q^{14} + 80 q^{16} - 40 q^{19} - 4 q^{20} + 8 q^{21} - 48 q^{24} - 2 q^{25} + 16 q^{26} - 40 q^{29} + 22 q^{30} + 50 q^{31} - 4 q^{34} + 4 q^{35} + 44 q^{36} - 56 q^{39} + 24 q^{40} + 42 q^{41} - 28 q^{44} + 46 q^{45} + 28 q^{46} - 34 q^{49} + 26 q^{50} + 8 q^{51} - 56 q^{54} + 12 q^{55} - 40 q^{59} + 78 q^{60} + 46 q^{61} - 148 q^{64} + 24 q^{65} - 52 q^{66} - 56 q^{69} + 12 q^{70} + 28 q^{71} - 32 q^{74} + 28 q^{75} + 96 q^{76} - 84 q^{79} + 76 q^{80} + 82 q^{81} - 20 q^{84} + 4 q^{85} - 140 q^{86} - 40 q^{89} + 188 q^{90} + 22 q^{91} - 108 q^{94} + 48 q^{95} + 8 q^{96} - 88 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
239.1 − 2.75044i − 0.411873i −5.56492 0.537920 + 2.17040i −1.13283 1.00000i 9.80510i 2.83036 5.96956 − 1.47952i
239.2 − 2.71765i − 1.53239i −5.38560 0.902877 − 2.04568i −4.16450 − 1.00000i 9.20085i 0.651775 −5.55944 − 2.45370i
239.3 − 2.60458i 1.96202i −4.78385 −1.92603 + 1.13595i 5.11025 − 1.00000i 7.25077i −0.849540 2.95868 + 5.01652i
239.4 − 2.59164i 2.79305i −4.71662 −0.187527 − 2.22819i 7.23859 1.00000i 7.04052i −4.80113 −5.77468 + 0.486004i
239.5 − 2.49820i 2.44484i −4.24100 2.11254 + 0.732919i 6.10770 − 1.00000i 5.59846i −2.97726 1.83098 − 5.27755i
239.6 − 2.31018i − 3.17334i −3.33691 0.277696 − 2.21876i −7.33098 1.00000i 3.08850i −7.07012 −5.12572 − 0.641527i
239.7 − 1.78766i − 1.15029i −1.19572 −1.70978 − 1.44107i −2.05633 − 1.00000i − 1.43778i 1.67682 −2.57613 + 3.05649i
239.8 − 1.73588i 2.27912i −1.01328 2.21898 + 0.275914i 3.95627 1.00000i − 1.71282i −2.19437 0.478954 − 3.85188i
239.9 − 1.66143i − 0.751043i −0.760334 −0.218024 + 2.22541i −1.24780 − 1.00000i − 2.05961i 2.43593 3.69736 + 0.362231i
239.10 − 1.47536i 3.25411i −0.176702 −2.14338 − 0.637104i 4.80100 − 1.00000i − 2.69003i −7.58924 −0.939961 + 3.16227i
239.11 − 1.27120i − 2.05725i 0.384039 −1.63957 − 1.52047i −2.61519 1.00000i − 3.03060i −1.23230 −1.93282 + 2.08423i
239.12 − 1.23485i − 1.50392i 0.475153 −1.36482 + 1.77123i −1.85711 1.00000i − 3.05644i 0.738223 2.18720 + 1.68535i
239.13 − 0.941615i 0.631977i 1.11336 1.90777 + 1.16636i 0.595079 − 1.00000i − 2.93159i 2.60061 1.09827 − 1.79639i
239.14 − 0.624680i − 3.32843i 1.60978 −2.10174 − 0.763339i −2.07920 − 1.00000i − 2.25495i −8.07842 −0.476842 + 1.31292i
239.15 − 0.602648i 0.0327837i 1.63682 2.06630 + 0.854629i 0.0197570 1.00000i − 2.19172i 2.99893 0.515040 − 1.24525i
239.16 − 0.208967i 2.86423i 1.95633 1.71447 − 1.43548i 0.598530 − 1.00000i − 0.826742i −5.20384 −0.299968 − 0.358266i
239.17 − 0.0232963i 2.43648i 1.99946 0.552321 − 2.16678i 0.0567609 1.00000i − 0.0931724i −2.93644 −0.0504779 − 0.0128670i
239.18 0.0232963i − 2.43648i 1.99946 0.552321 + 2.16678i 0.0567609 − 1.00000i 0.0931724i −2.93644 −0.0504779 + 0.0128670i
239.19 0.208967i − 2.86423i 1.95633 1.71447 + 1.43548i 0.598530 1.00000i 0.826742i −5.20384 −0.299968 + 0.358266i
239.20 0.602648i − 0.0327837i 1.63682 2.06630 − 0.854629i 0.0197570 − 1.00000i 2.19172i 2.99893 0.515040 + 1.24525i
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 239.34
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 595.2.c.b ✓ 34
5.b even 2 1 inner 595.2.c.b ✓ 34
5.c odd 4 1 2975.2.a.x 17
5.c odd 4 1 2975.2.a.y 17
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
595.2.c.b ✓ 34 1.a even 1 1 trivial
595.2.c.b ✓ 34 5.b even 2 1 inner
2975.2.a.x 17 5.c odd 4 1
2975.2.a.y 17 5.c odd 4 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{34} + 56 T_{2}^{32} + 1414 T_{2}^{30} + 21294 T_{2}^{28} + 213229 T_{2}^{26} + 1498928 T_{2}^{24} + \cdots + 36 \) acting on \(S_{2}^{\mathrm{new}}(595, [\chi])\). Copy content Toggle raw display