↑

Properties

Label 79.3.d.a
Level $79$
Weight $3$
Character orbit 79.d
Analytic conductor $2.153$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [79,3,Mod(24,79)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(79, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("79.24");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 79 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 79.d (of order \(6\), degree \(2\), 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: \(2.15259408845\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 2 q^{2} - 14 q^{4} - q^{5} - 3 q^{6} - 6 q^{7} + 32 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 2 q^{2} - 14 q^{4} - q^{5} - 3 q^{6} - 6 q^{7} + 32 q^{8} + 28 q^{9} - 68 q^{10} - 7 q^{11} + 5 q^{13} - 54 q^{16} - 32 q^{18} + 16 q^{19} + 74 q^{20} - 214 q^{21} + 40 q^{22} + 30 q^{23} + 192 q^{24} - 7 q^{25} + 85 q^{26} + 159 q^{28} + 21 q^{29} - 213 q^{30} + 67 q^{31} - 121 q^{32} + 27 q^{34} - 60 q^{35} - 29 q^{36} + 168 q^{37} - 2 q^{38} - 21 q^{39} + 47 q^{40} + 11 q^{42} - 258 q^{43} + 15 q^{44} - 55 q^{45} + 176 q^{46} + 36 q^{47} - 288 q^{48} + 74 q^{49} + 18 q^{50} + 82 q^{51} - 356 q^{52} - 90 q^{53} - 96 q^{54} - 95 q^{55} - 159 q^{56} - 309 q^{59} + 735 q^{60} + 10 q^{62} + 48 q^{63} + 304 q^{64} + 262 q^{65} + 84 q^{66} + 292 q^{67} + 63 q^{68} + 360 q^{70} + 83 q^{72} - 292 q^{73} - 144 q^{74} + 123 q^{75} + 124 q^{76} + 630 q^{77} + 154 q^{79} - 774 q^{80} - 92 q^{81} - 579 q^{82} + 54 q^{83} + 231 q^{84} + 72 q^{85} + 396 q^{86} - 658 q^{87} - 316 q^{88} - 354 q^{89} - 362 q^{90} - 82 q^{92} - 141 q^{95} - 100 q^{97} + 315 q^{98} + 353 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
24.1 −1.91907 + 3.32392i 3.47568 + 2.00668i −5.36565 − 9.29358i 3.16863 + 5.48823i −13.3401 + 7.70193i −7.25539 + 4.18890i 25.8357 3.55356 + 6.15495i −24.3233
24.2 −1.64931 + 2.85669i −1.98647 − 1.14689i −3.44046 − 5.95905i −1.24123 − 2.14987i 6.55263 − 3.78316i 5.85262 − 3.37901i 9.50306 −1.86928 − 3.23769i 8.18868
24.3 −1.09040 + 1.88863i −1.47876 − 0.853760i −0.377953 − 0.654633i 2.33882 + 4.05096i 3.22488 − 1.86188i −6.51112 + 3.75920i −7.07473 −3.04219 − 5.26922i −10.2010
24.4 −0.896335 + 1.55250i 3.41691 + 1.97276i 0.393169 + 0.680988i 0.0675475 + 0.116996i −6.12540 + 3.53650i 6.42856 − 3.71153i −8.58032 3.28353 + 5.68724i −0.242181
24.5 −0.459723 + 0.796263i −2.81700 − 1.62639i 1.57731 + 2.73198i −3.39699 − 5.88376i 2.59008 − 1.49538i −7.43651 + 4.29347i −6.57828 0.790321 + 1.36888i 6.24669
24.6 −0.215043 + 0.372465i −5.11355 − 2.95231i 1.90751 + 3.30391i 2.52541 + 4.37413i 2.19926 − 1.26974i 9.53932 − 5.50753i −3.36113 12.9323 + 22.3993i −2.17228
24.7 −0.172251 + 0.298348i 1.82544 + 1.05392i 1.94066 + 3.36132i −0.0557645 − 0.0965870i −0.628868 + 0.363077i −2.67748 + 1.54585i −2.71513 −2.27851 − 3.94650i 0.0384220
24.8 0.668125 − 1.15723i 0.0214011 + 0.0123559i 1.10722 + 1.91776i 3.43096 + 5.94260i 0.0285972 − 0.0165106i 0.388483 − 0.224291i 8.30404 −4.49969 − 7.79370i 9.16923
24.9 0.685160 − 1.18673i −0.536456 − 0.309723i 1.06111 + 1.83790i −4.55393 − 7.88764i −0.735117 + 0.424420i 9.84103 − 5.68172i 8.38941 −4.30814 − 7.46192i −12.4807
24.10 0.829318 − 1.43642i 4.40488 + 2.54316i 0.624463 + 1.08160i −2.89732 − 5.01831i 7.30609 − 4.21817i −8.46316 + 4.88621i 8.70606 8.43530 + 14.6104i −9.61121
24.11 1.48526 − 2.57254i −3.27715 − 1.89206i −2.41198 − 4.17768i −0.600126 − 1.03945i −9.73483 + 5.62041i −1.09637 + 0.632987i −2.44760 2.65981 + 4.60693i −3.56537
24.12 1.73427 − 3.00385i 2.06508 + 1.19227i −4.01540 − 6.95488i 0.713991 + 1.23667i 7.16281 − 4.13545i −1.60999 + 0.929527i −13.9810 −1.65697 − 2.86996i 4.95302
56.1 −1.91907 − 3.32392i 3.47568 − 2.00668i −5.36565 + 9.29358i 3.16863 − 5.48823i −13.3401 − 7.70193i −7.25539 − 4.18890i 25.8357 3.55356 − 6.15495i −24.3233
56.2 −1.64931 − 2.85669i −1.98647 + 1.14689i −3.44046 + 5.95905i −1.24123 + 2.14987i 6.55263 + 3.78316i 5.85262 + 3.37901i 9.50306 −1.86928 + 3.23769i 8.18868
56.3 −1.09040 − 1.88863i −1.47876 + 0.853760i −0.377953 + 0.654633i 2.33882 − 4.05096i 3.22488 + 1.86188i −6.51112 − 3.75920i −7.07473 −3.04219 + 5.26922i −10.2010
56.4 −0.896335 − 1.55250i 3.41691 − 1.97276i 0.393169 − 0.680988i 0.0675475 − 0.116996i −6.12540 − 3.53650i 6.42856 + 3.71153i −8.58032 3.28353 − 5.68724i −0.242181
56.5 −0.459723 − 0.796263i −2.81700 + 1.62639i 1.57731 − 2.73198i −3.39699 + 5.88376i 2.59008 + 1.49538i −7.43651 − 4.29347i −6.57828 0.790321 − 1.36888i 6.24669
56.6 −0.215043 − 0.372465i −5.11355 + 2.95231i 1.90751 − 3.30391i 2.52541 − 4.37413i 2.19926 + 1.26974i 9.53932 + 5.50753i −3.36113 12.9323 − 22.3993i −2.17228
56.7 −0.172251 − 0.298348i 1.82544 − 1.05392i 1.94066 − 3.36132i −0.0557645 + 0.0965870i −0.628868 − 0.363077i −2.67748 − 1.54585i −2.71513 −2.27851 + 3.94650i 0.0384220
56.8 0.668125 + 1.15723i 0.0214011 − 0.0123559i 1.10722 − 1.91776i 3.43096 − 5.94260i 0.0285972 + 0.0165106i 0.388483 + 0.224291i 8.30404 −4.49969 + 7.79370i 9.16923
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 24.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
79.d odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 79.3.d.a ✓ 24
79.d odd 6 1 inner 79.3.d.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
79.3.d.a ✓ 24 1.a even 1 1 trivial
79.3.d.a ✓ 24 79.d odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(79, [\chi])\).