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Properties

Label 29.10.d.a
Level $29$
Weight $10$
Character orbit 29.d
Analytic conductor $14.936$
Analytic rank $0$
Dimension $126$
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] = [29,10,Mod(7,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.7");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 29.d (of order \(7\), degree \(6\), 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: \(14.9360392488\)
Analytic rank: \(0\)
Dimension: \(126\)
Relative dimension: \(21\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 126 q - 23 q^{2} - 5 q^{3} - 4699 q^{4} - 1031 q^{5} + 12781 q^{6} - 4959 q^{7} - 43354 q^{8} - 76050 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 126 q - 23 q^{2} - 5 q^{3} - 4699 q^{4} - 1031 q^{5} + 12781 q^{6} - 4959 q^{7} - 43354 q^{8} - 76050 q^{9} + 8859 q^{10} - 195479 q^{11} + 141544 q^{12} - 68475 q^{13} - 271695 q^{14} + 322691 q^{15} - 916571 q^{16} - 587320 q^{17} - 3205692 q^{18} + 172239 q^{19} + 3022721 q^{20} + 4240955 q^{21} - 4806212 q^{22} + 4136729 q^{23} + 8763829 q^{24} + 3929026 q^{25} - 8916101 q^{26} - 22233347 q^{27} - 5636492 q^{28} - 8783106 q^{29} - 13875058 q^{30} + 4440751 q^{31} + 50266340 q^{32} - 13013201 q^{33} + 16498997 q^{34} + 2015357 q^{35} - 85629988 q^{36} + 3514043 q^{37} + 14330570 q^{38} - 72230993 q^{39} + 133179859 q^{40} + 16544588 q^{41} - 137066822 q^{42} + 51166115 q^{43} - 29984908 q^{44} + 263764053 q^{45} + 383616568 q^{46} - 97798039 q^{47} - 402814002 q^{48} + 35450702 q^{49} + 7192792 q^{50} + 57784388 q^{51} + 602315978 q^{52} + 137607435 q^{53} + 125382220 q^{54} - 411109327 q^{55} - 407148817 q^{56} - 138815986 q^{57} - 723336259 q^{58} - 899263700 q^{59} + 447938680 q^{60} + 666491883 q^{61} + 1037044473 q^{62} - 190916493 q^{63} + 65021266 q^{64} + 1392512087 q^{65} - 1056293177 q^{66} - 903332019 q^{67} - 1632042348 q^{68} - 527752591 q^{69} - 682041198 q^{70} + 1107000159 q^{71} + 430010561 q^{72} + 657123873 q^{73} - 198127908 q^{74} - 2404866172 q^{75} - 2839934913 q^{76} - 45301525 q^{77} + 2634791081 q^{78} + 1783807493 q^{79} + 3968800932 q^{80} + 2649824196 q^{81} + 3528483524 q^{82} - 1900496455 q^{83} - 3681471661 q^{84} + 183497446 q^{85} + 1213703072 q^{86} - 4480302165 q^{87} - 3448461606 q^{88} - 2924525111 q^{89} + 6284889126 q^{90} + 3601999725 q^{91} + 1893443670 q^{92} - 961083481 q^{93} + 1812573594 q^{94} + 837629545 q^{95} - 6708668090 q^{96} + 4263408987 q^{97} + 1842677548 q^{98} - 1747477852 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 −8.91229 − 39.0473i 127.724 + 61.5086i −983.966 + 473.853i −236.965 − 1038.21i 1263.43 − 5535.46i −2677.25 − 1289.29i 14486.6 + 18165.6i 257.944 + 323.451i −38427.5 + 18505.7i
7.2 −8.73749 − 38.2814i −154.771 − 74.5340i −927.828 + 446.819i 87.4849 + 383.296i −1500.95 + 6576.11i 1543.32 + 743.222i 12677.0 + 15896.5i 6126.74 + 7682.69i 13908.7 − 6698.09i
7.3 −7.97654 − 34.9475i 73.3338 + 35.3157i −696.407 + 335.372i 440.975 + 1932.04i 649.245 − 2844.53i −672.333 − 323.778i 5832.25 + 7313.41i −8141.50 − 10209.1i 64002.5 − 30822.0i
7.4 −5.87345 − 25.7333i 26.9577 + 12.9821i −166.408 + 80.1377i −430.743 − 1887.21i 175.738 − 769.959i 11130.5 + 5360.17i −5386.41 − 6754.35i −11714.0 − 14688.9i −46034.1 + 22168.8i
7.5 −5.54005 − 24.2726i −131.756 − 63.4505i −97.1687 + 46.7940i −324.293 − 1420.82i −810.169 + 3549.58i −5845.17 − 2814.89i −6273.59 − 7866.83i 1061.61 + 1331.22i −32690.3 + 15742.8i
7.6 −4.51238 − 19.7700i 207.546 + 99.9488i 90.8034 − 43.7286i 242.704 + 1063.35i 1039.46 − 4554.19i 7696.37 + 3706.38i −7747.68 − 9715.29i 20813.3 + 26099.1i 19927.4 − 9596.52i
7.7 −3.60417 − 15.7909i 194.806 + 93.8135i 224.933 − 108.322i −195.891 − 858.256i 779.288 − 3414.28i −8317.05 − 4005.28i −7691.72 − 9645.11i 16876.1 + 21162.0i −12846.6 + 6186.61i
7.8 −3.55763 − 15.5870i −34.2508 − 16.4943i 230.999 − 111.243i 376.920 + 1651.40i −135.245 + 592.548i −3361.64 − 1618.88i −7659.50 − 9604.70i −11371.1 − 14258.9i 24399.3 − 11750.1i
7.9 −2.47449 − 10.8414i −225.022 − 108.365i 349.882 − 168.494i 219.969 + 963.748i −618.017 + 2707.71i 8189.04 + 3943.63i −6242.39 − 7827.70i 26619.8 + 33380.1i 9904.11 − 4769.57i
7.10 0.385822 + 1.69040i 56.2085 + 27.0686i 458.587 − 220.844i −382.587 − 1676.22i −24.0702 + 105.458i −3478.73 − 1675.27i 1103.74 + 1384.05i −9845.46 − 12345.8i 2685.87 − 1293.45i
7.11 0.627749 + 2.75035i 11.2588 + 5.42194i 454.126 − 218.695i −3.74500 − 16.4079i −7.84454 + 34.3692i 4557.29 + 2194.68i 1787.13 + 2240.99i −12174.8 − 15266.7i 42.7766 − 20.6001i
7.12 1.74711 + 7.65458i −184.828 − 89.0086i 405.756 − 195.402i −360.877 − 1581.11i 358.408 − 1570.29i −2780.15 − 1338.85i 4711.00 + 5907.41i 13966.8 + 17513.8i 11472.2 − 5524.73i
7.13 3.16487 + 13.8662i 167.309 + 80.5715i 279.040 − 134.379i 294.188 + 1288.92i −587.712 + 2574.94i 197.795 + 95.2529i 7286.76 + 9137.30i 9228.22 + 11571.8i −16941.4 + 8158.56i
7.14 3.51960 + 15.4204i −156.258 − 75.2501i 235.896 − 113.601i 407.649 + 1786.03i 610.417 − 2674.41i −9946.82 − 4790.14i 7631.23 + 9569.25i 6481.96 + 8128.12i −26106.5 + 12572.2i
7.15 5.60294 + 24.5481i 216.248 + 104.140i −109.919 + 52.9341i −599.659 − 2627.28i −1344.80 + 5891.96i 6165.53 + 2969.16i 6122.63 + 7677.54i 23646.0 + 29651.2i 61134.7 − 29440.9i
7.16 5.62456 + 24.6428i −142.401 − 68.5766i −114.336 + 55.0612i −253.940 − 1112.59i 888.978 − 3894.87i 4795.80 + 2309.54i 6069.00 + 7610.28i 3303.10 + 4141.95i 25988.9 − 12515.6i
7.17 6.40812 + 28.0758i −74.0782 − 35.6742i −285.891 + 137.678i 487.167 + 2134.42i 526.879 − 2308.41i 7791.48 + 3752.18i 3495.59 + 4383.34i −8057.22 − 10103.4i −56803.7 + 27355.2i
7.18 6.98240 + 30.5919i 109.509 + 52.7366i −425.814 + 205.061i 98.6572 + 432.245i −848.680 + 3718.31i −9851.07 − 4744.03i 770.482 + 966.154i −3061.13 − 3838.54i −12534.3 + 6036.22i
7.19 7.92629 + 34.7274i −14.5980 − 7.03001i −681.868 + 328.370i −247.282 − 1083.41i 128.426 − 562.671i −1483.34 − 714.340i −5437.11 − 6817.92i −12108.5 − 15183.5i 35664.0 − 17174.9i
7.20 9.66013 + 42.3238i 159.134 + 76.6349i −1236.69 + 595.558i 242.294 + 1061.56i −1706.22 + 7475.46i 6300.89 + 3034.35i −23294.5 − 29210.4i 7178.56 + 9001.63i −42588.6 + 20509.6i
See next 80 embeddings (of 126 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 7.21
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.d even 7 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 29.10.d.a ✓ 126
29.d even 7 1 inner 29.10.d.a ✓ 126
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
29.10.d.a ✓ 126 1.a even 1 1 trivial
29.10.d.a ✓ 126 29.d even 7 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(29, [\chi])\).