Properties

Label 29.14.b.a
Level $29$
Weight $14$
Character orbit 29.b
Analytic conductor $31.097$
Analytic rank $0$
Dimension $32$
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] = [29,14,Mod(28,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.28");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 29.b (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: \(31.0969693961\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 131436 q^{4} - 90794 q^{5} - 191952 q^{6} + 398260 q^{7} - 18624674 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 131436 q^{4} - 90794 q^{5} - 191952 q^{6} + 398260 q^{7} - 18624674 q^{9} + 5240482 q^{13} + 549733588 q^{16} + 593107012 q^{20} - 1351453384 q^{22} + 1866943772 q^{23} + 4550583596 q^{24} + 7169723618 q^{25} - 13976463456 q^{28} - 10157197956 q^{29} + 21508715952 q^{30} - 8142086534 q^{33} + 21000232616 q^{34} - 15057663628 q^{35} + 116060443480 q^{36} - 86572746688 q^{38} + 13537077480 q^{42} + 263177965664 q^{45} + 513778986120 q^{49} - 372662169044 q^{51} - 101448215388 q^{52} + 573910354530 q^{53} + 1479431015408 q^{54} + 500871600416 q^{57} - 969686686880 q^{58} + 1024205768724 q^{59} + 1751113369840 q^{62} - 4168751771256 q^{63} - 2804312517964 q^{64} - 781490399506 q^{65} - 872679676184 q^{67} - 1363415929136 q^{71} - 6756459308672 q^{74} - 23715100786248 q^{78} + 1267893681036 q^{80} + 25379587936536 q^{81} + 4236061808312 q^{82} + 6421393088172 q^{83} - 16601603597496 q^{86} + 3240260232764 q^{87} + 3526967972716 q^{88} - 5472886962916 q^{91} + 1684734140256 q^{92} + 3555997675886 q^{93} + 29362958775032 q^{94} - 39622013504436 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
28.1 172.131i 162.472i −21436.9 −30311.5 27966.4 −275351. 2.27986e6i 1.56793e6 5.21754e6i
28.2 170.335i 2487.01i −20822.1 −14654.1 −423626. 377681. 2.15135e6i −4.59090e6 2.49611e6i
28.3 162.205i 2079.21i −18118.4 28499.1 337258. 310872. 1.61011e6i −2.72878e6 4.62269e6i
28.4 150.378i 424.630i −14421.4 51875.3 −63854.8 −9683.03 936765.i 1.41401e6 7.80089e6i
28.5 132.025i 277.645i −9238.68 −56763.6 36656.1 461874. 138188.i 1.51724e6 7.49423e6i
28.6 126.947i 1277.29i −7923.52 −10445.6 162148. −142325. 34082.3i −37154.7 1.32604e6i
28.7 126.142i 1441.05i −7719.68 18388.4 −181776. −251905. 59579.3i −482306. 2.31954e6i
28.8 98.6070i 1104.52i −1531.33 −7305.52 −108914. 327252. 656788.i 374351. 720375.i
28.9 98.5448i 1929.16i −1519.09 −5197.51 190109. −337055. 657581.i −2.12734e6 512188.i
28.10 93.2678i 1663.21i −506.883 −63620.5 −155124. −566395. 716774.i −1.17195e6 5.93374e6i
28.11 67.0223i 954.542i 3700.01 48346.3 63975.5 444756. 797030.i 683173. 3.24028e6i
28.12 53.0296i 485.442i 5379.86 48264.8 25742.8 −490607. 719711.i 1.35867e6 2.55946e6i
28.13 36.6487i 2214.40i 6848.87 −60644.2 81155.0 368083. 551229.i −3.30925e6 2.22253e6i
28.14 33.2848i 1160.53i 7084.12 −2193.20 −38628.1 222431. 508463.i 247490. 73000.2i
28.15 32.2136i 483.965i 7154.29 −28573.6 15590.2 −142510. 494358.i 1.36010e6 920457.i
28.16 28.9666i 2232.02i 7352.94 38938.5 −64654.1 −97987.5 450284.i −3.38761e6 1.12791e6i
28.17 28.9666i 2232.02i 7352.94 38938.5 −64654.1 −97987.5 450284.i −3.38761e6 1.12791e6i
28.18 32.2136i 483.965i 7154.29 −28573.6 15590.2 −142510. 494358.i 1.36010e6 920457.i
28.19 33.2848i 1160.53i 7084.12 −2193.20 −38628.1 222431. 508463.i 247490. 73000.2i
28.20 36.6487i 2214.40i 6848.87 −60644.2 81155.0 368083. 551229.i −3.30925e6 2.22253e6i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 28.32
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 29.14.b.a 32
29.b even 2 1 inner 29.14.b.a 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
29.14.b.a 32 1.a even 1 1 trivial
29.14.b.a 32 29.b even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{14}^{\mathrm{new}}(29, [\chi])\).