↑

Properties

Label 23.19.d.a
Level $23$
Weight $19$
Character orbit 23.d
Analytic conductor $47.239$
Analytic rank $0$
Dimension $350$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [23,19,Mod(5,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 19, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.5");
 
S:= CuspForms(chi, 19);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 23.d (of order \(22\), degree \(10\), 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: \(47.2388116732\)
Analytic rank: \(0\)
Dimension: \(350\)
Relative dimension: \(35\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 350 q - 179 q^{2} + 20119 q^{3} - 4092083 q^{4} - 11 q^{5} - 2318126 q^{6} - 11 q^{7} - 18825206 q^{8} - 4214797052 q^{9} - 11 q^{10} - 11 q^{11} + 5321755786 q^{12} + 655768935 q^{13} - 11 q^{14} + 253448904621 q^{15}+ \cdots - 95\!\cdots\!51 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 −972.723 − 285.617i −21289.0 + 24568.8i 644082. + 413927.i −2.61874e6 − 376518.i 2.77256e7 − 1.78182e7i 3.10489e7 − 1.41796e7i −3.34254e8 − 3.85750e8i −9.52698e7 − 6.62616e8i 2.43977e9 + 1.11420e9i
5.2 −891.456 − 261.755i 5322.19 − 6142.13i 505648. + 324961.i −224350. − 32256.6i −6.35223e6 + 4.08233e6i −3.58399e7 + 1.63675e7i −2.06208e8 − 2.37977e8i 4.57356e7 + 3.18098e8i 1.91555e8 + 8.74800e7i
5.3 −879.175 − 258.149i 23921.7 − 27607.1i 485778. + 312191.i −974965. − 140179.i −2.81581e7 + 1.80961e7i 2.92849e7 − 1.33739e7i −1.89195e8 − 2.18342e8i −1.34770e8 − 9.37344e8i 8.20978e8 + 3.74928e8i
5.4 −834.018 − 244.890i −6332.43 + 7308.02i 415086. + 266759.i 1.27505e6 + 183325.i 7.07102e6 − 4.54427e6i −6.57423e6 + 3.00235e6i −1.31644e8 − 1.51925e8i 4.18283e7 + 2.90922e8i −1.01852e9 − 4.65144e8i
5.5 −813.243 − 238.790i 5160.86 − 5955.95i 383814. + 246662.i 2.73369e6 + 393045.i −5.61925e6 + 3.61127e6i 6.24972e7 − 2.85415e7i −1.07732e8 − 1.24329e8i 4.62968e7 + 3.22001e8i −2.12930e9 − 9.72418e8i
5.6 −705.605 − 207.184i −21958.0 + 25340.9i 234424. + 150655.i 2.86413e6 + 411799.i 2.07439e7 − 1.33313e7i −1.89187e7 + 8.63986e6i −7.95388e6 − 9.17927e6i −1.04871e8 − 7.29392e8i −1.93562e9 − 8.83970e8i
5.7 −661.855 − 194.338i 5870.72 − 6775.17i 179755. + 115521.i −3.81094e6 − 547930.i −5.20224e6 + 3.34328e6i −1.09178e7 + 4.98598e6i 2.18945e7 + 2.52676e7i 4.36981e7 + 3.03927e8i 2.41580e9 + 1.10326e9i
5.8 −600.804 − 176.412i −14313.6 + 16518.7i 109315. + 70252.3i −817661. − 117562.i 1.15138e7 − 7.39944e6i −2.96412e7 + 1.35367e7i 5.42096e7 + 6.25612e7i −1.28549e7 − 8.94077e7i 4.70515e8 + 2.14877e8i
5.9 −591.122 − 173.569i 18020.4 − 20796.7i 98769.1 + 63475.1i 2.99880e6 + 431163.i −1.42619e7 + 9.16557e6i −5.80033e7 + 2.64892e7i 5.83933e7 + 6.73895e7i −5.26303e7 − 3.66052e8i −1.69782e9 − 7.75369e8i
5.10 −583.928 − 171.457i −9265.85 + 10693.4i 91045.2 + 58511.2i −1.09148e6 − 156932.i 7.24404e6 − 4.65546e6i 6.93679e7 − 3.16793e7i 6.13419e7 + 7.07923e7i 2.66437e7 + 1.85311e8i 6.10441e8 + 2.78779e8i
5.11 −523.477 − 153.707i 15666.4 − 18079.9i 29872.9 + 19198.1i −423720. − 60921.7i −1.09800e7 + 7.05641e6i 7.00584e6 − 3.19946e6i 8.09711e7 + 9.34456e7i −2.63138e7 − 1.83016e8i 2.12444e8 + 9.70197e7i
5.12 −310.050 − 91.0388i 14960.1 − 17264.9i −132687. − 85272.6i 85207.5 + 12251.0i −6.21014e6 + 3.99102e6i 2.90055e7 − 1.32464e7i 8.88490e7 + 1.02537e8i −1.91356e7 − 1.33091e8i −2.53033e7 − 1.15556e7i
5.13 −280.355 − 82.3196i −2850.60 + 3289.77i −148707. − 95568.3i 972005. + 139753.i 1.06999e6 − 687642.i −1.73624e7 + 7.92913e6i 8.39834e7 + 9.69220e7i 5.24390e7 + 3.64721e8i −2.61002e8 − 1.19196e8i
5.14 −247.435 − 72.6536i −2002.81 + 2311.37i −164584. − 105772.i 3.73299e6 + 536723.i 663496. − 426403.i 1.64144e7 − 7.49620e6i 7.73091e7 + 8.92195e7i 5.38045e7 + 3.74219e8i −8.84679e8 − 4.04020e8i
5.15 −167.402 − 49.1537i −20577.1 + 23747.3i −194922. − 125269.i −2.67014e6 − 383909.i 4.61193e6 − 2.96391e6i −3.86539e6 + 1.76527e6i 5.64238e7 + 6.51165e7i −8.53793e7 − 5.93826e8i 4.28118e8 + 1.95515e8i
5.16 −139.648 − 41.0043i −19251.5 + 22217.4i −202709. − 130273.i 1.62951e6 + 234288.i 3.59943e6 − 2.31322e6i 4.00472e7 − 1.82890e7i 4.79512e7 + 5.53387e7i −6.78573e7 − 4.71958e8i −2.17951e8 − 9.95347e7i
5.17 −96.1002 − 28.2176i −1918.13 + 2213.63i −212091. − 136302.i −623805. − 89689.6i 246796. − 158606.i −7.28887e7 + 3.32871e7i 3.37296e7 + 3.89260e7i 5.39147e7 + 3.74985e8i 5.74170e7 + 2.62214e7i
5.18 −37.5676 − 11.0308i 24217.8 − 27948.8i −219240. − 140897.i −2.98990e6 − 429883.i −1.21810e6 + 782827.i −5.94063e7 + 2.71300e7i 1.34035e7 + 1.54685e7i −1.39499e8 − 9.70239e8i 1.07581e8 + 4.91308e7i
5.19 39.3893 + 11.5657i 6199.14 − 7154.19i −219112. − 140815.i −2.05139e6 − 294945.i 326923. − 210101.i 2.62723e7 − 1.19982e7i −1.40494e7 − 1.62138e7i 4.23826e7 + 2.94777e8i −7.73915e7 − 3.53435e7i
5.20 163.114 + 47.8946i 20807.8 − 24013.5i −196217. − 126101.i 1.95816e6 + 281541.i 4.54415e6 − 2.92035e6i 3.27588e7 − 1.49604e7i −5.51497e7 − 6.36462e7i −8.85467e7 − 6.15856e8i 3.05919e8 + 1.39709e8i
See next 80 embeddings (of 350 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.35
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.d odd 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 23.19.d.a ✓ 350
23.d odd 22 1 inner 23.19.d.a ✓ 350
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.19.d.a ✓ 350 1.a even 1 1 trivial
23.19.d.a ✓ 350 23.d odd 22 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{19}^{\mathrm{new}}(23, [\chi])\).