Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,4,Mod(29,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.29");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.n (of order \(10\), degree \(4\), 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: | \(10.3253342510\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Relative dimension: | \(46\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
29.1 | −5.33970 | − | 1.73497i | 4.27738 | − | 5.88731i | 19.0301 | + | 13.8262i | 0.958148 | + | 11.1392i | −33.0542 | + | 24.0153i | − | 7.00000i | −51.2260 | − | 70.5065i | −8.02097 | − | 24.6860i | 14.2100 | − | 61.1423i | |
29.2 | −5.13942 | − | 1.66990i | −6.05549 | + | 8.33466i | 17.1529 | + | 12.4623i | −8.87502 | + | 6.79956i | 45.0397 | − | 32.7232i | 7.00000i | −41.9344 | − | 57.7178i | −24.4542 | − | 75.2623i | 56.9670 | − | 20.1254i | ||
29.3 | −4.84806 | − | 1.57523i | −0.337638 | + | 0.464719i | 14.5502 | + | 10.5713i | −10.4623 | − | 3.94223i | 2.36893 | − | 1.72113i | − | 7.00000i | −29.9179 | − | 41.1784i | 8.24149 | + | 25.3647i | 44.5117 | + | 35.5927i | |
29.4 | −4.60786 | − | 1.49718i | 3.74866 | − | 5.15959i | 12.5187 | + | 9.09533i | 0.431164 | − | 11.1720i | −24.9981 | + | 18.1622i | 7.00000i | −21.2843 | − | 29.2953i | −4.22544 | − | 13.0046i | −18.7133 | + | 50.8336i | ||
29.5 | −4.33997 | − | 1.41014i | −3.60118 | + | 4.95660i | 10.3747 | + | 7.53768i | 1.08940 | − | 11.1271i | 22.6185 | − | 16.4333i | − | 7.00000i | −12.9388 | − | 17.8087i | −3.25592 | − | 10.0207i | −20.4188 | + | 46.7553i | |
29.6 | −4.20035 | − | 1.36478i | 3.35106 | − | 4.61233i | 9.30816 | + | 6.76277i | −11.0102 | + | 1.94320i | −20.3704 | + | 14.8000i | 7.00000i | −9.10018 | − | 12.5253i | −1.70057 | − | 5.23383i | 48.8986 | + | 6.86429i | ||
29.7 | −4.17415 | − | 1.35626i | 3.72842 | − | 5.13173i | 9.11197 | + | 6.62023i | 7.05167 | − | 8.67606i | −22.5230 | + | 16.3639i | − | 7.00000i | −8.41781 | − | 11.5861i | −4.09005 | − | 12.5879i | −41.2018 | + | 26.6513i | |
29.8 | −4.14674 | − | 1.34736i | −0.156667 | + | 0.215634i | 8.90794 | + | 6.47200i | 2.85591 | + | 10.8094i | 0.940194 | − | 0.683091i | 7.00000i | −7.71622 | − | 10.6205i | 8.32151 | + | 25.6110i | 2.72147 | − | 48.6718i | ||
29.9 | −3.84227 | − | 1.24843i | −1.96796 | + | 2.70866i | 6.73233 | + | 4.89132i | −7.97675 | + | 7.83399i | 10.9430 | − | 7.95056i | − | 7.00000i | −0.763719 | − | 1.05117i | 4.87946 | + | 15.0174i | 40.4290 | − | 20.1419i | |
29.10 | −3.51045 | − | 1.14062i | −4.79433 | + | 6.59884i | 4.55015 | + | 3.30588i | 9.23381 | + | 6.30371i | 24.3570 | − | 17.6964i | − | 7.00000i | 5.15429 | + | 7.09427i | −12.2155 | − | 37.5955i | −25.2248 | − | 32.6611i | |
29.11 | −3.25824 | − | 1.05867i | −4.08903 | + | 5.62807i | 3.02324 | + | 2.19651i | −2.61627 | − | 10.8699i | 19.2813 | − | 14.0087i | 7.00000i | 8.58456 | + | 11.8156i | −6.61154 | − | 20.3482i | −2.98320 | + | 38.1866i | ||
29.12 | −3.14628 | − | 1.02229i | 5.97409 | − | 8.22263i | 2.38186 | + | 1.73053i | 9.51619 | + | 5.86874i | −27.2020 | + | 19.7634i | 7.00000i | 9.83115 | + | 13.5314i | −23.5784 | − | 72.5669i | −23.9411 | − | 28.1930i | ||
29.13 | −3.12049 | − | 1.01391i | 2.53633 | − | 3.49096i | 2.23733 | + | 1.62551i | 9.52039 | + | 5.86193i | −11.4541 | + | 8.32191i | − | 7.00000i | 10.0951 | + | 13.8947i | 2.58962 | + | 7.97003i | −23.7648 | − | 27.9449i | |
29.14 | −2.68802 | − | 0.873391i | −1.95014 | + | 2.68413i | −0.00948949 | − | 0.00689452i | −11.1618 | − | 0.642777i | 7.58631 | − | 5.51177i | 7.00000i | 13.3098 | + | 18.3194i | 4.94192 | + | 15.2097i | 29.4419 | + | 11.4765i | ||
29.15 | −2.47630 | − | 0.804598i | 5.46136 | − | 7.51692i | −0.987463 | − | 0.717434i | −11.1800 | + | 0.0843389i | −19.5720 | + | 14.2199i | − | 7.00000i | 14.1115 | + | 19.4228i | −18.3341 | − | 56.4266i | 27.7529 | + | 8.78657i | |
29.16 | −2.19780 | − | 0.714108i | 0.650083 | − | 0.894762i | −2.15176 | − | 1.56335i | 9.81277 | − | 5.35813i | −2.06771 | + | 1.50228i | 7.00000i | 14.4793 | + | 19.9290i | 7.96547 | + | 24.5152i | −25.3928 | + | 4.76872i | ||
29.17 | −1.89034 | − | 0.614210i | 1.45093 | − | 1.99704i | −3.27599 | − | 2.38015i | −2.33690 | + | 10.9334i | −3.96936 | + | 2.88391i | − | 7.00000i | 14.0772 | + | 19.3756i | 6.46051 | + | 19.8834i | 11.1329 | − | 19.2325i | |
29.18 | −1.45329 | − | 0.472202i | −4.11709 | + | 5.66669i | −4.58306 | − | 3.32979i | 7.99330 | + | 7.81711i | 8.65915 | − | 6.29124i | 7.00000i | 12.2736 | + | 16.8932i | −6.81747 | − | 20.9820i | −7.92531 | − | 15.1350i | ||
29.19 | −1.16040 | − | 0.377036i | −2.32250 | + | 3.19665i | −5.26777 | − | 3.82726i | 8.39609 | − | 7.38279i | 3.90028 | − | 2.83372i | − | 7.00000i | 10.4070 | + | 14.3240i | 3.51891 | + | 10.8301i | −12.5264 | + | 5.40135i | |
29.20 | −0.648207 | − | 0.210615i | 3.20984 | − | 4.41796i | −6.09632 | − | 4.42924i | −5.06193 | + | 9.96880i | −3.01113 | + | 2.18771i | 7.00000i | 6.22373 | + | 8.56622i | −0.871872 | − | 2.68335i | 5.38076 | − | 5.39572i | ||
See next 80 embeddings (of 184 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
25.e | even | 10 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 175.4.n.a | ✓ | 184 |
25.e | even | 10 | 1 | inner | 175.4.n.a | ✓ | 184 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
175.4.n.a | ✓ | 184 | 1.a | even | 1 | 1 | trivial |
175.4.n.a | ✓ | 184 | 25.e | even | 10 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(175, [\chi])\).