↑

Properties

Label 103.14.a.b
Level $103$
Weight $14$
Character orbit 103.a
Self dual yes
Analytic conductor $110.448$
Analytic rank $0$
Dimension $58$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [103,14,Mod(1,103)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(103, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("103.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 103 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 103.a (trivial)

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: yes
Analytic conductor: \(110.447856820\)
Analytic rank: \(0\)
Dimension: \(58\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 58 q + 319 q^{2} + 2056 q^{3} + 241663 q^{4} + 99003 q^{5} + 15103 q^{6} + 590766 q^{7} + 4462404 q^{8} + 36178572 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 58 q + 319 q^{2} + 2056 q^{3} + 241663 q^{4} + 99003 q^{5} + 15103 q^{6} + 590766 q^{7} + 4462404 q^{8} + 36178572 q^{9} + 2772878 q^{10} + 8123351 q^{11} + 18896055 q^{12} + 59229655 q^{13} + 19213543 q^{14} + 41611927 q^{15} + 1091940219 q^{16} + 597043717 q^{17} + 569910072 q^{18} + 349543441 q^{19} + 971642589 q^{20} + 1180077538 q^{21} + 920963425 q^{22} + 3328532444 q^{23} + 210678066 q^{24} + 17852865629 q^{25} + 11310471885 q^{26} + 4762510072 q^{27} - 8077232192 q^{28} + 2584126324 q^{29} - 39398448850 q^{30} - 7760177888 q^{31} + 15758980372 q^{32} + 24147225719 q^{33} + 44809828870 q^{34} + 33577289133 q^{35} + 243148331760 q^{36} + 61090717256 q^{37} + 176159154978 q^{38} + 162350957493 q^{39} + 275826876731 q^{40} + 176939998854 q^{41} + 323324315395 q^{42} + 130967366354 q^{43} + 218880784232 q^{44} + 239097417200 q^{45} + 100137578113 q^{46} + 104175742097 q^{47} - 177069810447 q^{48} + 966124187962 q^{49} + 286676872954 q^{50} + 96534985995 q^{51} + 105473953239 q^{52} + 293155957803 q^{53} - 1741678100493 q^{54} - 71690700610 q^{55} - 891503272957 q^{56} + 37357722495 q^{57} - 1071961395110 q^{58} - 77321827829 q^{59} - 5152388766785 q^{60} - 375940541079 q^{61} - 556127068115 q^{62} - 830130932412 q^{63} - 709377041506 q^{64} + 3240866264071 q^{65} - 3776533328041 q^{66} - 445019354164 q^{67} + 3280976439900 q^{68} - 1282941625534 q^{69} - 6222955388960 q^{70} + 1661323892685 q^{71} + 4058759289214 q^{72} + 330656537593 q^{73} + 1124341253107 q^{74} + 4755967281311 q^{75} + 7515310203732 q^{76} + 7489149354027 q^{77} + 3329009596224 q^{78} + 6932814893435 q^{79} + 9372218887398 q^{80} + 27799532475098 q^{81} + 10516883057873 q^{82} + 12785357911311 q^{83} + 25973281099121 q^{84} + 5656258206903 q^{85} + 6577528277133 q^{86} + 10044505136332 q^{87} + 9477534119405 q^{88} + 22906961228218 q^{89} + 38860270851040 q^{90} + 9293214492391 q^{91} + 54876841883100 q^{92} + 38366420464976 q^{93} + 41866722336936 q^{94} + 28131030040682 q^{95} + 36410982637111 q^{96} + 33669362901648 q^{97} + 85378468355245 q^{98} + 40463908906842 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −167.699 −1960.75 19930.8 −4221.88 328816. 105688. −1.96859e6 2.25023e6 708004.
1.2 −164.880 −1296.48 18993.3 41287.1 213764. 150460. −1.78092e6 86549.5 −6.80740e6
1.3 −164.802 2410.42 18967.7 23587.5 −397241. 240103. −1.77585e6 4.21578e6 −3.88727e6
1.4 −163.278 −1397.79 18467.7 −63284.6 228228. −93738.0 −1.67780e6 359487. 1.03330e7
1.5 −160.510 2000.91 17571.5 −50972.4 −321167. −509532. −1.50551e6 2.40932e6 8.18159e6
1.6 −159.118 1062.10 17126.6 −22016.1 −168999. 30260.3 −1.42166e6 −466271. 3.50316e6
1.7 −141.051 −718.917 11703.3 34278.0 101404. 426079. −495270. −1.07748e6 −4.83494e6
1.8 −132.560 891.571 9380.09 52136.1 −118186. 594390. −157493. −799424. −6.91114e6
1.9 −132.538 1198.15 9374.22 −28306.5 −158800. 15776.8 −156689. −158760. 3.75168e6
1.10 −132.463 119.044 9354.51 −19066.0 −15769.0 92988.1 −153990. −1.58015e6 2.52554e6
1.11 −131.674 −1590.23 9146.10 66033.4 209393. −291090. −125631. 934518. −8.69490e6
1.12 −118.197 −461.093 5778.60 30249.2 54500.0 −329170. 285257. −1.38172e6 −3.57537e6
1.13 −114.361 −1605.29 4886.34 −46497.4 183581. −312891. 378037. 982620. 5.31747e6
1.14 −111.235 1866.64 4181.20 20397.7 −207635. −580095. 446141. 1.89001e6 −2.26894e6
1.15 −84.2691 2267.08 −1090.71 51053.4 −191045. −191795. 782246. 3.54533e6 −4.30223e6
1.16 −83.7898 −185.092 −1171.28 17270.1 15508.8 47218.4 784547. −1.56006e6 −1.44706e6
1.17 −67.6669 −576.954 −3613.19 −44014.7 39040.7 546091. 798821. −1.26145e6 2.97834e6
1.18 −64.9634 −1746.99 −3971.76 15040.7 113491. −206104. 790199. 1.45767e6 −977092.
1.19 −62.7828 −1468.74 −4250.32 −34909.2 92211.3 −97247.9 781164. 562860. 2.19169e6
1.20 −62.1530 644.369 −4329.00 −25163.7 −40049.5 −488151. 778218. −1.17911e6 1.56400e6
See all 58 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.58
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(103\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 103.14.a.b ✓ 58
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
103.14.a.b ✓ 58 1.a even 1 1 trivial