Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(25,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(40\) 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
25.1 | −3.24066 | − | 4.46038i | −2.34848 | − | 7.22789i | −6.92102 | + | 21.3007i | −7.96782 | + | 10.9668i | −24.6285 | + | 33.8982i | −23.0659 | − | 7.49455i | 75.4900 | − | 24.5282i | −24.8835 | + | 18.0789i | 74.7369 | ||
25.2 | −3.05502 | − | 4.20487i | −0.605039 | − | 1.86212i | −5.87568 | + | 18.0835i | 6.52386 | − | 8.97932i | −5.98157 | + | 8.23292i | 15.3171 | + | 4.97683i | 54.4441 | − | 17.6900i | 18.7420 | − | 13.6169i | −57.6874 | ||
25.3 | −2.99746 | − | 4.12565i | 2.67526 | + | 8.23360i | −5.56408 | + | 17.1245i | −11.3048 | + | 15.5597i | 25.9500 | − | 35.7171i | 1.89146 | + | 0.614574i | 48.5278 | − | 15.7676i | −38.7917 | + | 28.1838i | 98.0794 | ||
25.4 | −2.97823 | − | 4.09918i | 1.04463 | + | 3.21504i | −5.46131 | + | 16.8082i | 2.66533 | − | 3.66851i | 10.0679 | − | 13.8572i | −6.84110 | − | 2.22281i | 46.6138 | − | 15.1457i | 12.5982 | − | 9.15316i | −22.9758 | ||
25.5 | −2.58109 | − | 3.55257i | 2.03748 | + | 6.27072i | −3.48657 | + | 10.7306i | 5.87800 | − | 8.09037i | 17.0182 | − | 23.4236i | −2.32170 | − | 0.754367i | 13.7098 | − | 4.45460i | −13.3271 | + | 9.68270i | −43.9133 | ||
25.6 | −2.47563 | − | 3.40741i | −1.83607 | − | 5.65083i | −3.00956 | + | 9.26247i | −5.13780 | + | 7.07158i | −14.7093 | + | 20.2456i | 23.0063 | + | 7.47520i | 6.96637 | − | 2.26351i | −6.71728 | + | 4.88039i | 36.8150 | ||
25.7 | −2.35953 | − | 3.24761i | −3.09622 | − | 9.52919i | −2.50747 | + | 7.71720i | 8.33529 | − | 11.4725i | −23.6415 | + | 32.5397i | 7.59080 | + | 2.46640i | 0.436537 | − | 0.141839i | −59.3754 | + | 43.1388i | −56.9257 | ||
25.8 | −2.34047 | − | 3.22138i | 0.168906 | + | 0.519839i | −2.42734 | + | 7.47059i | −6.24582 | + | 8.59663i | 1.27928 | − | 1.76078i | −28.0425 | − | 9.11157i | −0.548925 | + | 0.178357i | 21.6018 | − | 15.6946i | 42.3111 | ||
25.9 | −2.07518 | − | 2.85624i | −1.29150 | − | 3.97482i | −1.37961 | + | 4.24599i | 2.94180 | − | 4.04904i | −8.67296 | + | 11.9373i | −10.2208 | − | 3.32095i | −11.8712 | + | 3.85719i | 7.71220 | − | 5.60324i | −17.6698 | ||
25.10 | −2.03051 | − | 2.79476i | 0.161025 | + | 0.495585i | −1.21557 | + | 3.74113i | −8.96888 | + | 12.3446i | 1.05808 | − | 1.45632i | 16.3193 | + | 5.30246i | −13.3597 | + | 4.34083i | 21.6238 | − | 15.7106i | 52.7116 | ||
25.11 | −1.84899 | − | 2.54492i | 2.52460 | + | 7.76993i | −0.585700 | + | 1.80260i | 2.53463 | − | 3.48862i | 15.1059 | − | 20.7914i | 31.9374 | + | 10.3771i | −18.2634 | + | 5.93414i | −32.1547 | + | 23.3618i | −13.5647 | ||
25.12 | −1.38497 | − | 1.90624i | −0.928232 | − | 2.85681i | 0.756503 | − | 2.32828i | 7.86101 | − | 10.8197i | −4.16020 | + | 5.72602i | −12.3082 | − | 3.99917i | −23.4134 | + | 7.60747i | 14.5437 | − | 10.5666i | −31.5123 | ||
25.13 | −1.34014 | − | 1.84454i | 1.90248 | + | 5.85523i | 0.865771 | − | 2.66457i | 10.8950 | − | 14.9957i | 8.25063 | − | 11.3560i | −23.1527 | − | 7.52276i | −23.4223 | + | 7.61036i | −8.82081 | + | 6.40869i | −42.2611 | ||
25.14 | −1.17535 | − | 1.61773i | 1.36382 | + | 4.19741i | 1.23654 | − | 3.80567i | −5.85576 | + | 8.05976i | 5.18729 | − | 7.13970i | −0.00726186 | − | 0.00235952i | −22.8239 | + | 7.41594i | 6.08525 | − | 4.42119i | 19.9210 | ||
25.15 | −1.00857 | − | 1.38817i | −2.62521 | − | 8.07958i | 1.56232 | − | 4.80832i | −2.93663 | + | 4.04193i | −8.56815 | + | 11.7930i | −18.0190 | − | 5.85473i | −21.3057 | + | 6.92263i | −36.5444 | + | 26.5511i | 8.57268 | ||
25.16 | −0.959626 | − | 1.32081i | −0.156611 | − | 0.482000i | 1.64847 | − | 5.07348i | 11.1106 | − | 15.2925i | −0.486343 | + | 0.669394i | 30.6277 | + | 9.95155i | −20.7047 | + | 6.72736i | 21.6357 | − | 15.7192i | −30.8606 | ||
25.17 | −0.879569 | − | 1.21062i | 3.03153 | + | 9.33009i | 1.78017 | − | 5.47880i | −4.73233 | + | 6.51349i | 8.62878 | − | 11.8765i | −22.9824 | − | 7.46744i | −19.5839 | + | 6.36320i | −56.0169 | + | 40.6986i | 12.0478 | ||
25.18 | −0.638353 | − | 0.878617i | −2.31620 | − | 7.12853i | 2.10766 | − | 6.48672i | −10.7701 | + | 14.8238i | −4.78470 | + | 6.58557i | 6.75722 | + | 2.19555i | −15.3078 | + | 4.97380i | −23.6077 | + | 17.1520i | 19.8996 | ||
25.19 | −0.313996 | − | 0.432179i | 1.17154 | + | 3.60564i | 2.38395 | − | 7.33705i | −4.60303 | + | 6.33553i | 1.19042 | − | 1.63847i | 4.31855 | + | 1.40318i | −7.98392 | + | 2.59413i | 10.2153 | − | 7.42187i | 4.18341 | ||
25.20 | −0.249988 | − | 0.344080i | −1.06869 | − | 3.28909i | 2.41624 | − | 7.43642i | −0.222452 | + | 0.306179i | −0.864547 | + | 1.18995i | 24.1058 | + | 7.83243i | −6.39867 | + | 2.07905i | 12.1675 | − | 8.84018i | 0.160960 | ||
See next 80 embeddings (of 160 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
11.c | even | 5 | 1 | inner |
13.b | even | 2 | 1 | inner |
143.n | even | 10 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 143.4.n.a | ✓ | 160 |
11.c | even | 5 | 1 | inner | 143.4.n.a | ✓ | 160 |
13.b | even | 2 | 1 | inner | 143.4.n.a | ✓ | 160 |
143.n | even | 10 | 1 | inner | 143.4.n.a | ✓ | 160 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
143.4.n.a | ✓ | 160 | 1.a | even | 1 | 1 | trivial |
143.4.n.a | ✓ | 160 | 11.c | even | 5 | 1 | inner |
143.4.n.a | ✓ | 160 | 13.b | even | 2 | 1 | inner |
143.4.n.a | ✓ | 160 | 143.n | even | 10 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(143, [\chi])\).