Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,10,Mod(2,23)]
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([2]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.2");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.c (of order \(11\), 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: | \(11.8458242318\) |
Analytic rank: | \(0\) |
Dimension: | \(170\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{11})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2.1 | −37.2704 | − | 23.9522i | 17.9475 | + | 124.827i | 602.681 | + | 1319.69i | 1413.32 | + | 414.989i | 2320.98 | − | 5082.24i | −7622.70 | + | 8797.06i | 5919.11 | − | 41168.3i | 3625.96 | − | 1064.68i | −42735.1 | − | 49319.0i |
2.2 | −31.7148 | − | 20.3818i | −5.04104 | − | 35.0612i | 377.715 | + | 827.080i | −472.249 | − | 138.665i | −554.737 | + | 1214.70i | 7160.89 | − | 8264.11i | 2131.30 | − | 14823.5i | 17681.8 | − | 5191.85i | 12151.0 | + | 14023.0i |
2.3 | −26.6551 | − | 17.1302i | −29.0863 | − | 202.300i | 204.359 | + | 447.484i | 210.621 | + | 61.8440i | −2690.14 | + | 5890.58i | −3087.20 | + | 3562.81i | −90.4594 | + | 629.159i | −21193.5 | + | 6222.98i | −4554.74 | − | 5256.45i |
2.4 | −23.7212 | − | 15.2447i | 20.3997 | + | 141.883i | 117.602 | + | 257.513i | −2176.95 | − | 639.211i | 1679.06 | − | 3676.62i | −2868.99 | + | 3310.99i | −918.575 | + | 6388.83i | −828.913 | + | 243.391i | 41895.4 | + | 48349.8i |
2.5 | −19.3117 | − | 12.4109i | 32.9551 | + | 229.208i | 6.22000 | + | 13.6199i | 1344.48 | + | 394.774i | 2208.25 | − | 4835.40i | 4195.31 | − | 4841.65i | −1623.77 | + | 11293.6i | −32564.4 | + | 9561.77i | −21064.7 | − | 24309.9i |
2.6 | −14.3223 | − | 9.20438i | −1.55598 | − | 10.8221i | −92.2849 | − | 202.076i | 1543.83 | + | 453.310i | −77.3256 | + | 169.319i | −1288.91 | + | 1487.48i | −1778.78 | + | 12371.7i | 18771.0 | − | 5511.66i | −17938.8 | − | 20702.5i |
2.7 | −5.08899 | − | 3.27050i | −22.3597 | − | 155.515i | −197.491 | − | 432.445i | −2066.95 | − | 606.911i | −394.824 | + | 864.544i | 137.421 | − | 158.592i | −850.062 | + | 5912.31i | −4799.38 | + | 1409.22i | 8533.78 | + | 9848.51i |
2.8 | −3.75865 | − | 2.41553i | 3.02788 | + | 21.0594i | −204.400 | − | 447.573i | −84.8947 | − | 24.9273i | 39.4889 | − | 86.4687i | −1251.63 | + | 1444.46i | −638.417 | + | 4440.29i | 18451.4 | − | 5417.81i | 258.876 | + | 298.759i |
2.9 | 2.27840 | + | 1.46424i | −34.9692 | − | 243.216i | −209.645 | − | 459.059i | 1977.74 | + | 580.717i | 276.452 | − | 605.346i | 7648.62 | − | 8826.98i | 391.860 | − | 2725.44i | −39045.5 | + | 11464.8i | 3655.77 | + | 4218.98i |
2.10 | 7.63720 | + | 4.90813i | 33.3373 | + | 231.866i | −178.455 | − | 390.763i | −458.130 | − | 134.519i | −883.424 | + | 1934.43i | −5366.11 | + | 6192.82i | 1216.51 | − | 8461.03i | −33764.7 | + | 9914.20i | −2838.60 | − | 3275.91i |
2.11 | 8.38475 | + | 5.38855i | 19.8184 | + | 137.840i | −171.425 | − | 375.368i | −910.049 | − | 267.214i | −576.587 | + | 1262.55i | 6824.79 | − | 7876.23i | 1311.58 | − | 9122.25i | 278.549 | − | 81.7895i | −6190.63 | − | 7144.37i |
2.12 | 15.2974 | + | 9.83105i | −1.23691 | − | 8.60291i | −75.3311 | − | 164.952i | 1465.21 | + | 430.225i | 65.6541 | − | 143.762i | −3094.73 | + | 3571.51i | 1794.27 | − | 12479.4i | 18813.2 | − | 5524.06i | 18184.4 | + | 20985.9i |
2.13 | 19.2422 | + | 12.3662i | −28.9842 | − | 201.590i | 4.64721 | + | 10.1760i | −323.193 | − | 94.8980i | 1935.18 | − | 4237.46i | −6396.47 | + | 7381.92i | 1630.25 | − | 11338.6i | −20912.7 | + | 6140.52i | −5045.42 | − | 5822.73i |
2.14 | 24.1470 | + | 15.5184i | −11.1258 | − | 77.3816i | 129.568 | + | 283.713i | −1221.63 | − | 358.703i | 932.181 | − | 2041.19i | 4026.47 | − | 4646.80i | 817.403 | − | 5685.16i | 13021.6 | − | 3823.48i | −23932.3 | − | 27619.3i |
2.15 | 27.3293 | + | 17.5635i | 24.5672 | + | 170.869i | 225.721 | + | 494.261i | 2459.29 | + | 722.112i | −2329.64 | + | 5101.20i | 3138.36 | − | 3621.86i | −145.002 | + | 1008.51i | −9706.90 | + | 2850.20i | 54527.7 | + | 62928.3i |
2.16 | 32.1827 | + | 20.6826i | 19.4420 | + | 135.222i | 395.267 | + | 865.514i | −1263.96 | − | 371.131i | −2171.05 | + | 4753.93i | −2843.93 | + | 3282.07i | −2392.79 | + | 16642.2i | 978.645 | − | 287.356i | −33001.6 | − | 38085.9i |
2.17 | 35.8106 | + | 23.0141i | −23.3833 | − | 162.634i | 540.060 | + | 1182.57i | 1123.63 | + | 329.927i | 2905.51 | − | 6362.18i | 1437.36 | − | 1658.80i | −4774.07 | + | 33204.4i | −7017.38 | + | 2060.49i | 32644.8 | + | 37674.1i |
3.1 | −5.68739 | − | 39.5567i | −6.59512 | + | 14.4413i | −1041.12 | + | 305.701i | −439.442 | + | 507.143i | 608.758 | + | 178.748i | 370.747 | − | 238.264i | 9513.86 | + | 20832.5i | 12724.6 | + | 14684.9i | 22560.2 | + | 14498.5i |
3.2 | −5.05902 | − | 35.1863i | 93.0827 | − | 203.823i | −721.220 | + | 211.769i | 966.721 | − | 1115.66i | −7642.67 | − | 2244.09i | −2470.85 | + | 1587.92i | 3539.23 | + | 7749.84i | −19989.7 | − | 23069.4i | −44146.4 | − | 28371.2i |
3.3 | −4.42307 | − | 30.7631i | −74.9596 | + | 164.139i | −435.545 | + | 127.888i | 1553.11 | − | 1792.39i | 5380.97 | + | 1579.99i | −2794.08 | + | 1795.65i | −749.704 | − | 1641.62i | −8432.94 | − | 9732.14i | −62008.9 | − | 39850.7i |
See next 80 embeddings (of 170 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
23.c | even | 11 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 23.10.c.a | ✓ | 170 |
23.c | even | 11 | 1 | inner | 23.10.c.a | ✓ | 170 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
23.10.c.a | ✓ | 170 | 1.a | even | 1 | 1 | trivial |
23.10.c.a | ✓ | 170 | 23.c | even | 11 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(23, [\chi])\).