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Properties

Label 79.7.d.a
Level $79$
Weight $7$
Character orbit 79.d
Analytic conductor $18.174$
Analytic rank $0$
Dimension $78$
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] = [79,7,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, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("79.24");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 79 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(18.1742726060\)
Analytic rank: \(0\)
Dimension: \(78\)
Relative dimension: \(39\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 78 q - 6 q^{2} - 3 q^{3} - 1130 q^{4} - q^{5} - 3 q^{6} + 225 q^{7} + 1104 q^{8} + 9406 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 78 q - 6 q^{2} - 3 q^{3} - 1130 q^{4} - q^{5} - 3 q^{6} + 225 q^{7} + 1104 q^{8} + 9406 q^{9} + 292 q^{10} - 1897 q^{11} - 3861 q^{13} - 31670 q^{16} + 2944 q^{18} + 4863 q^{19} + 37294 q^{20} + 46106 q^{21} + 96784 q^{22} - 12929 q^{23} - 67308 q^{24} - 78812 q^{25} - 9083 q^{26} - 61629 q^{28} - 24291 q^{29} - 3273 q^{30} - 86861 q^{31} + 43111 q^{32} - 41265 q^{34} + 164565 q^{35} + 252859 q^{36} + 44769 q^{37} + 105142 q^{38} - 281571 q^{39} - 235993 q^{40} + 77147 q^{42} - 329067 q^{43} - 45885 q^{44} + 21410 q^{45} - 308024 q^{46} - 312603 q^{47} - 52188 q^{48} + 710274 q^{49} + 195258 q^{50} - 401360 q^{51} + 450788 q^{52} + 220341 q^{53} - 27024 q^{54} - 163955 q^{55} - 1932255 q^{56} - 177483 q^{59} + 3085755 q^{60} + 1029826 q^{62} + 1058034 q^{63} + 483296 q^{64} - 707378 q^{65} - 230568 q^{66} - 203180 q^{67} - 1449657 q^{68} + 2734260 q^{70} - 49885 q^{72} + 202887 q^{73} + 1479468 q^{74} - 1897692 q^{75} - 1067176 q^{76} + 411573 q^{77} - 635314 q^{79} - 1352374 q^{80} - 143183 q^{81} - 416943 q^{82} - 200225 q^{83} - 3888021 q^{84} + 115272 q^{85} + 203952 q^{86} - 662854 q^{87} - 3920140 q^{88} + 269068 q^{89} - 249842 q^{90} + 933994 q^{92} + 2756309 q^{95} - 3560756 q^{97} - 331169 q^{98} + 1140518 q^{99}+O(q^{100}) \) 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 −7.69937 + 13.3357i 7.58674 + 4.38021i −86.5607 − 149.927i 2.20697 + 3.82258i −116.826 + 67.4497i 165.625 − 95.6234i 1680.33 −326.128 − 564.870i −67.9691
24.2 −7.48903 + 12.9714i −37.5750 − 21.6939i −80.1710 − 138.860i −51.8276 − 89.7680i 562.800 − 324.933i −5.10865 + 2.94948i 1443.02 576.754 + 998.967i 1552.55
24.3 −6.91880 + 11.9837i 33.1125 + 19.1175i −63.7395 − 110.400i −28.8766 − 50.0158i −458.197 + 264.540i −491.993 + 284.052i 878.397 366.458 + 634.723i 799.166
24.4 −6.62109 + 11.4681i −20.0584 − 11.5807i −55.6778 − 96.4367i 96.2866 + 166.773i 265.617 − 153.354i −500.503 + 288.965i 627.091 −96.2733 − 166.750i −2550.09
24.5 −6.38185 + 11.0537i 4.71959 + 2.72486i −49.4561 − 85.6605i 55.3826 + 95.9255i −60.2395 + 34.7793i 101.607 − 58.6627i 445.609 −349.650 − 605.612i −1413.77
24.6 −6.25052 + 10.8262i 43.6983 + 25.2293i −46.1379 − 79.9132i 94.9774 + 164.506i −546.274 + 315.392i 369.396 − 213.271i 353.477 908.530 + 1573.62i −2374.63
24.7 −6.10275 + 10.5703i −7.09161 − 4.09434i −42.4871 − 73.5898i −98.2844 − 170.234i 86.5566 − 49.9735i 199.992 − 115.465i 256.001 −330.973 − 573.262i 2399.22
24.8 −5.64209 + 9.77239i −35.2604 − 20.3576i −31.6664 − 54.8478i 28.2628 + 48.9526i 397.884 − 229.719i 170.323 − 98.3361i −7.52907 464.363 + 804.300i −637.845
24.9 −5.24398 + 9.08285i 28.1743 + 16.2664i −22.9987 − 39.8350i −69.9632 − 121.180i −295.491 + 170.602i 66.6162 − 38.4609i −188.810 164.694 + 285.259i 1467.54
24.10 −4.42416 + 7.66287i −16.7486 − 9.66979i −7.14642 − 12.3780i −67.1509 − 116.309i 148.197 − 85.5614i −438.696 + 253.281i −439.825 −177.490 − 307.422i 1188.35
24.11 −4.13572 + 7.16328i −4.49521 − 2.59531i −2.20838 − 3.82503i 43.9043 + 76.0445i 37.1819 − 21.4670i 522.338 − 301.572i −492.839 −351.029 − 608.000i −726.304
24.12 −3.51708 + 6.09176i 17.0846 + 9.86379i 7.26027 + 12.5752i 92.1259 + 159.567i −120.176 + 69.3835i −246.501 + 142.317i −552.326 −169.911 − 294.295i −1296.06
24.13 −3.11872 + 5.40179i −31.4303 − 18.1463i 12.5471 + 21.7323i 42.9231 + 74.3449i 196.045 − 113.186i 180.467 − 104.193i −555.721 294.074 + 509.351i −535.461
24.14 −2.99465 + 5.18688i 34.1598 + 19.7222i 14.0642 + 24.3599i −53.2646 − 92.2570i −204.593 + 118.122i 400.957 − 231.493i −551.784 413.427 + 716.076i 638.035
24.15 −2.83087 + 4.90322i 24.5529 + 14.1756i 15.9723 + 27.6648i 14.0855 + 24.3968i −139.013 + 80.2589i −242.741 + 140.147i −543.214 37.3978 + 64.7749i −159.497
24.16 −1.67743 + 2.90539i −3.35143 − 1.93495i 26.3725 + 45.6785i −16.5149 − 28.6046i 11.2435 − 6.49146i −68.7615 + 39.6995i −391.662 −357.012 − 618.363i 110.810
24.17 −1.41157 + 2.44492i −44.8568 − 25.8981i 28.0149 + 48.5233i −22.0757 − 38.2362i 126.637 − 73.1141i −377.499 + 217.949i −338.862 976.924 + 1692.08i 124.646
24.18 −1.15532 + 2.00108i −32.2224 − 18.6036i 29.3305 + 50.8018i −111.704 − 193.477i 74.4545 − 42.9863i 454.923 − 262.650i −283.426 327.687 + 567.571i 516.218
24.19 0.0352702 − 0.0610898i −25.5832 − 14.7704i 31.9975 + 55.4213i 116.040 + 200.987i −1.80465 + 1.04191i −24.8601 + 14.3530i 9.02882 71.8321 + 124.417i 16.3710
24.20 0.0443419 − 0.0768024i 43.3006 + 24.9996i 31.9961 + 55.4188i 29.1396 + 50.4713i 3.84006 − 2.21706i −117.659 + 67.9302i 11.3508 885.461 + 1533.66i 5.16842
See all 78 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 24.39
Significant digits:
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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 79.7.d.a ✓ 78
79.d odd 6 1 inner 79.7.d.a ✓ 78
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
79.7.d.a ✓ 78 1.a even 1 1 trivial
79.7.d.a ✓ 78 79.d odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(79, [\chi])\).