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Properties

Label 23.17.d.a
Level $23$
Weight $17$
Character orbit 23.d
Analytic conductor $37.335$
Analytic rank $0$
Dimension $310$
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] = [23,17,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, 17, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.5");
 
S:= CuspForms(chi, 17);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 17 \)
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: \(37.3346450870\)
Analytic rank: \(0\)
Dimension: \(310\)
Relative dimension: \(31\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 310 q - 195 q^{2} - 7919 q^{3} - 1005683 q^{4} - 11 q^{5} + 2268610 q^{6} - 11 q^{7} + 3539330 q^{8} - 478783694 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 310 q - 195 q^{2} - 7919 q^{3} - 1005683 q^{4} - 11 q^{5} + 2268610 q^{6} - 11 q^{7} + 3539330 q^{8} - 478783694 q^{9} - 11 q^{10} - 11 q^{11} - 774493430 q^{12} - 451093351 q^{13} - 11 q^{14} + 12152089092 q^{15} - 80101764379 q^{16} + 19673081494 q^{17} - 103535537550 q^{18} + 28069995712 q^{19} + 116253130741 q^{20} - 269655282644 q^{21} + 423659986604 q^{23} - 165662759734 q^{24} + 378917826672 q^{25} + 1258340067530 q^{26} + 942371019892 q^{27} - 832007700491 q^{28} - 1229952497418 q^{29} + 3925191852021 q^{30} + 1301222197256 q^{31} - 3687389059499 q^{32} + 9325683117894 q^{33} - 15462442158097 q^{34} + 9854614438957 q^{35} - 61724207942663 q^{36} + 29813993918709 q^{37} + 11019619240234 q^{38} - 38262561180317 q^{39} - 21553503125011 q^{40} + 19809162199137 q^{41} + 94769887187239 q^{42} - 50638409339595 q^{43} - 152847518739366 q^{44} + 275512774717005 q^{46} + 12108700285486 q^{47} - 98965492590886 q^{48} - 91442086294194 q^{49} + 31531587739224 q^{50} + 188897493178933 q^{51} + 721443811798728 q^{52} + 26427491680117 q^{53} - 11\!\cdots\!14 q^{54}+ \cdots - 24\!\cdots\!12 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 −468.737 − 137.634i −3961.06 + 4571.31i 145639. + 93596.5i 554346. + 79703.0i 2.48586e6 − 1.59757e6i −2.78651e6 + 1.27256e6i −3.44183e7 − 3.97209e7i 919324. + 6.39404e6i −2.48873e8 − 1.13656e8i
5.2 −444.125 − 130.407i 1418.34 − 1636.85i 125108. + 80402.3i −395259. − 56829.7i −843374. + 542004.i 5.13077e6 − 2.34315e6i −2.52136e7 − 2.90980e7i 5.45860e6 + 3.79654e7i 1.68133e8 + 7.67840e7i
5.3 −421.392 − 123.732i 5803.44 − 6697.52i 107129. + 68847.8i −155243. − 22320.6i −3.27422e6 + 2.10421e6i −7.32412e6 + 3.34481e6i −1.77764e7 − 2.05151e7i −5.05075e6 − 3.51287e7i 6.26564e7 + 2.86142e7i
5.4 −383.223 − 112.525i −3491.25 + 4029.12i 79066.0 + 50812.6i −219545. − 31565.9i 1.79130e6 − 1.15120e6i 4.70676e6 − 2.14951e6i −7.44117e6 − 8.58756e6i 2.08123e6 + 1.44752e7i 8.05830e7 + 3.68010e7i
5.5 −381.866 − 112.126i 6597.38 − 7613.78i 78117.3 + 50203.0i 650506. + 93528.6i −3.37302e6 + 2.16771e6i 4.90297e6 − 2.23911e6i −7.12091e6 − 8.21796e6i −8.31806e6 − 5.78534e7i −2.37919e8 − 1.08654e8i
5.6 −367.920 − 108.031i −6175.83 + 7127.29i 68561.9 + 44062.1i −512798. − 73729.2i 3.04218e6 − 1.95509e6i −9.72979e6 + 4.44345e6i −4.00861e6 − 4.62618e6i −6.53116e6 − 4.54252e7i 1.80704e8 + 8.25245e7i
5.7 −310.443 − 91.1544i 1527.54 − 1762.88i 32933.5 + 21165.1i 331994. + 47733.6i −634909. + 408031.i −789819. + 360698.i 5.59106e6 + 6.45243e6i 5.35183e6 + 3.72228e7i −9.87142e7 − 4.50813e7i
5.8 −303.634 − 89.1550i −8292.78 + 9570.38i 29112.6 + 18709.6i 170905. + 24572.5i 3.37122e6 − 2.16655e6i 8.35234e6 − 3.81439e6i 6.40964e6 + 7.39712e6i −1.66958e7 − 1.16122e8i −4.97019e7 − 2.26981e7i
5.9 −243.284 − 71.4347i 6665.07 − 7691.90i −1048.15 − 673.606i −440160. − 63285.5i −2.17097e6 + 1.39520e6i 8.52284e6 − 3.89225e6i 1.10887e7 + 1.27970e7i −8.61601e6 − 5.99256e7i 1.02563e8 + 4.68391e7i
5.10 −229.171 − 67.2906i −2799.12 + 3230.35i −7141.20 − 4589.37i 286635. + 41211.9i 858848. − 551948.i −522177. + 238470.i 1.15783e7 + 1.33620e7i 3.52606e6 + 2.45243e7i −6.29152e7 − 2.87324e7i
5.11 −202.768 − 59.5379i 2961.33 − 3417.56i −17562.5 − 11286.7i −294572. − 42353.1i −803937. + 516659.i −5.18696e6 + 2.36881e6i 1.19587e7 + 1.38010e7i 3.21596e6 + 2.23675e7i 5.72081e7 + 2.61260e7i
5.12 −129.709 − 38.0859i −1673.15 + 1930.92i −39758.6 − 25551.3i −660526. − 94969.4i 290563. − 186734.i 2.70103e6 − 1.23352e6i 9.98561e6 + 1.15240e7i 5.19717e6 + 3.61471e7i 8.20591e7 + 3.74751e7i
5.13 −89.6790 − 26.3321i 8020.15 − 9255.75i −47783.4 − 30708.6i 46103.5 + 6628.68i −962963. + 618859.i −2.53625e6 + 1.15827e6i 7.48779e6 + 8.64137e6i −1.52199e7 − 1.05856e8i −3.95997e6 − 1.80846e6i
5.14 −79.4595 − 23.3314i −6307.96 + 7279.78i −49362.9 − 31723.6i 568686. + 81764.8i 671076. − 431274.i −8.69886e6 + 3.97264e6i 6.73633e6 + 7.77414e6i −7.07858e6 − 4.92326e7i −4.32799e7 − 1.97653e7i
5.15 −50.8808 − 14.9399i −6161.60 + 7110.86i −52766.7 − 33911.1i −364881. − 52462.0i 419743. − 269752.i 1.33298e6 − 608751.i 4.45402e6 + 5.14021e6i −6.47290e6 − 4.50200e7i 1.77816e7 + 8.12061e6i
5.16 −22.9593 − 6.74145i 1833.82 − 2116.34i −54650.7 − 35121.9i 366467. + 52690.0i −56370.3 + 36227.0i 9.23349e6 − 4.21680e6i 2.04491e6 + 2.35995e6i 5.01019e6 + 3.48466e7i −8.05861e6 − 3.68024e6i
5.17 −7.24330 − 2.12683i 4677.56 − 5398.19i −55084.4 − 35400.6i 542648. + 78021.1i −45362.0 + 29152.4i −4.54573e6 + 2.07596e6i 647687. + 747470.i −1.13473e6 − 7.89222e6i −3.76463e6 − 1.71925e6i
5.18 70.2334 + 20.6224i −4429.14 + 5111.50i −50624.9 − 32534.7i 114072. + 16401.1i −416485. + 267659.i 3.59754e6 − 1.64294e6i −6.02608e6 − 6.95446e6i −383952. − 2.67045e6i 7.67344e6 + 3.50434e6i
5.19 113.756 + 33.4019i 4220.15 − 4870.32i −43307.6 − 27832.1i −471336. − 67768.0i 642747. − 413069.i −1.11970e6 + 511351.i −9.08505e6 − 1.04847e7i 215895. + 1.50158e6i −5.13539e7 − 2.34526e7i
5.20 116.916 + 34.3297i −1360.17 + 1569.72i −42641.5 − 27404.0i −156902. − 22559.1i −212914. + 136832.i −7.78039e6 + 3.55318e6i −9.27424e6 − 1.07030e7i 5.51223e6 + 3.83384e7i −1.75700e7 − 8.02393e6i
See next 80 embeddings (of 310 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.31
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 23.17.d.a ✓ 310
23.d odd 22 1 inner 23.17.d.a ✓ 310
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.17.d.a ✓ 310 1.a even 1 1 trivial
23.17.d.a ✓ 310 23.d odd 22 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{17}^{\mathrm{new}}(23, [\chi])\).