Properties

Label 29.11.c.a
Level $29$
Weight $11$
Character orbit 29.c
Analytic conductor $18.425$
Analytic rank $0$
Dimension $48$
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] = [29,11,Mod(12,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.12");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 29.c (of order \(4\), 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: \(18.4253603275\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 8 q^{2} - 2 q^{3} - 4 q^{7} + 76770 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 8 q^{2} - 2 q^{3} - 4 q^{7} + 76770 q^{8} + 109566 q^{10} - 263646 q^{11} + 729294 q^{12} + 502616 q^{14} - 721750 q^{15} - 16030232 q^{16} - 4538004 q^{17} + 3653906 q^{18} + 43692 q^{19} - 5378052 q^{20} + 17564076 q^{21} - 13984008 q^{23} + 1483608 q^{24} - 71407296 q^{25} + 39483006 q^{26} + 37745506 q^{27} - 81758188 q^{29} - 163829140 q^{30} + 80778630 q^{31} + 40419398 q^{32} - 404686536 q^{36} - 344948620 q^{37} - 133484166 q^{39} + 218842826 q^{40} - 408348748 q^{41} + 600101850 q^{43} + 1634309922 q^{44} - 905429108 q^{45} - 16491548 q^{46} + 469023202 q^{47} + 2697803274 q^{48} + 190419840 q^{49} - 944029470 q^{50} - 2515143720 q^{52} + 2546471244 q^{53} + 1710860632 q^{54} + 1558719146 q^{55} + 12187008 q^{56} - 1178304360 q^{58} - 220099600 q^{59} - 392429058 q^{60} + 1450673088 q^{61} + 578087196 q^{65} - 8698362294 q^{66} + 198241252 q^{68} - 8836922160 q^{69} - 6177008876 q^{70} + 14334525936 q^{72} + 4323265324 q^{73} + 9346881044 q^{74} + 16533837048 q^{75} - 8456818536 q^{76} - 851635980 q^{77} - 30331854672 q^{78} + 5001641754 q^{79} - 41499140164 q^{81} + 6276634960 q^{82} - 6714882896 q^{83} - 38944690012 q^{84} + 17632654432 q^{85} + 30089027578 q^{87} - 19890895724 q^{88} - 6965186344 q^{89} + 53283919568 q^{90} + 70296028628 q^{94} - 38341763060 q^{95} - 25903577492 q^{97} - 12739329192 q^{98} + 29044599948 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
12.1 −44.1507 44.1507i −258.692 258.692i 2874.56i 3209.07i 22842.8i −14020.3 81703.6 81703.6i 74794.0i 141682. 141682.i
12.2 −40.6077 40.6077i 280.280 + 280.280i 2273.97i 1637.07i 22763.0i 25799.0 50758.2 50758.2i 98064.8i 66477.5 66477.5i
12.3 −38.5476 38.5476i −40.6574 40.6574i 1947.84i 4037.41i 3134.49i 12255.5 35611.7 35611.7i 55743.0i −155633. + 155633.i
12.4 −36.5340 36.5340i 128.848 + 128.848i 1645.47i 1229.81i 9414.71i −26326.6 22704.9 22704.9i 25845.1i −44929.8 + 44929.8i
12.5 −30.2185 30.2185i −46.0531 46.0531i 802.313i 4207.29i 2783.31i 7518.31 −6699.05 + 6699.05i 54807.2i 127138. 127138.i
12.6 −27.5873 27.5873i −267.289 267.289i 498.124i 2802.28i 14747.6i 10208.5 −14507.5 + 14507.5i 83837.6i −77307.4 + 77307.4i
12.7 −17.7955 17.7955i 303.416 + 303.416i 390.637i 2124.43i 10798.9i −21311.3 −25174.2 + 25174.2i 125074.i 37805.4 37805.4i
12.8 −16.3961 16.3961i 189.226 + 189.226i 486.333i 5498.04i 6205.14i 9559.38 −24763.6 + 24763.6i 12563.6i −90146.7 + 90146.7i
12.9 −16.1017 16.1017i 130.144 + 130.144i 505.467i 1792.45i 4191.09i 14141.6 −24627.1 + 24627.1i 25174.1i 28861.6 28861.6i
12.10 −15.8431 15.8431i −149.513 149.513i 521.995i 249.743i 4737.47i −17394.4 −24493.3 + 24493.3i 14341.0i −3956.70 + 3956.70i
12.11 −2.46716 2.46716i −319.026 319.026i 1011.83i 5415.44i 1574.18i −6202.52 −5022.70 + 5022.70i 144507.i 13360.8 13360.8i
12.12 1.96929 + 1.96929i −66.5553 66.5553i 1016.24i 3811.80i 262.134i −21566.3 4017.83 4017.83i 50189.8i 7506.54 7506.54i
12.13 4.04305 + 4.04305i −142.774 142.774i 991.307i 351.494i 1154.48i 27728.5 8147.99 8147.99i 18280.4i 1421.11 1421.11i
12.14 4.76401 + 4.76401i 158.342 + 158.342i 978.608i 1411.74i 1508.68i 8006.05 9540.45 9540.45i 8904.77i −6725.56 + 6725.56i
12.15 8.23743 + 8.23743i 85.7567 + 85.7567i 888.289i 5766.16i 1412.83i −20112.5 15752.4 15752.4i 44340.6i −47498.4 + 47498.4i
12.16 18.1033 + 18.1033i 340.781 + 340.781i 368.538i 1274.81i 12338.5i 4091.64 25209.6 25209.6i 173214.i 23078.4 23078.4i
12.17 19.7480 + 19.7480i 136.340 + 136.340i 244.033i 2681.56i 5384.88i −4320.20 25041.1 25041.1i 21871.8i 52955.4 52955.4i
12.18 21.5476 + 21.5476i −331.286 331.286i 95.4007i 4922.29i 14276.9i −7134.44 24120.4 24120.4i 160452.i 106064. 106064.i
12.19 27.4558 + 27.4558i −172.516 172.516i 483.643i 2503.07i 9473.14i 5326.73 14835.9 14835.9i 474.609i −68723.9 + 68723.9i
12.20 29.1517 + 29.1517i −96.9833 96.9833i 675.640i 1089.69i 5654.45i −17667.0 10155.3 10155.3i 40237.5i −31766.3 + 31766.3i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 12.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.c odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 29.11.c.a 48
29.c odd 4 1 inner 29.11.c.a 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
29.11.c.a 48 1.a even 1 1 trivial
29.11.c.a 48 29.c odd 4 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(29, [\chi])\).