Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [190,3,Mod(29,190)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(190, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 17]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("190.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 190 = 2 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 190.o (of order \(18\), degree \(6\), 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: | \(5.17712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(120\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
$q$-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 | −0.245576 | − | 1.39273i | −3.99079 | + | 3.34867i | −1.87939 | + | 0.684040i | 2.53312 | − | 4.31083i | 5.64382 | + | 4.73573i | −8.01154 | − | 4.62547i | 1.41421 | + | 2.44949i | 3.14997 | − | 17.8644i | −6.62589 | − | 2.46931i |
29.2 | −0.245576 | − | 1.39273i | −3.88588 | + | 3.26064i | −1.87939 | + | 0.684040i | −3.86795 | + | 3.16843i | 5.49546 | + | 4.61124i | 3.11910 | + | 1.80081i | 1.41421 | + | 2.44949i | 2.90545 | − | 16.4776i | 5.36264 | + | 4.60892i |
29.3 | −0.245576 | − | 1.39273i | −2.27829 | + | 1.91171i | −1.87939 | + | 0.684040i | 3.94596 | + | 3.07073i | 3.22199 | + | 2.70357i | −5.25836 | − | 3.03592i | 1.41421 | + | 2.44949i | −0.0268715 | + | 0.152396i | 3.30766 | − | 6.24975i |
29.4 | −0.245576 | − | 1.39273i | −1.00496 | + | 0.843264i | −1.87939 | + | 0.684040i | −4.42892 | − | 2.32048i | 1.42123 | + | 1.19256i | 5.78989 | + | 3.34280i | 1.41421 | + | 2.44949i | −1.26398 | + | 7.16837i | −2.14417 | + | 6.73814i |
29.5 | −0.245576 | − | 1.39273i | −0.344931 | + | 0.289432i | −1.87939 | + | 0.684040i | 4.98850 | − | 0.338993i | 0.487806 | + | 0.409318i | 3.92642 | + | 2.26692i | 1.41421 | + | 2.44949i | −1.52763 | + | 8.66360i | −1.69718 | − | 6.86437i |
29.6 | −0.245576 | − | 1.39273i | 0.718479 | − | 0.602876i | −1.87939 | + | 0.684040i | −2.46682 | + | 4.34911i | −1.01608 | − | 0.852595i | −5.60642 | − | 3.23687i | 1.41421 | + | 2.44949i | −1.41008 | + | 7.99696i | 6.66293 | + | 2.36758i |
29.7 | −0.245576 | − | 1.39273i | 1.55916 | − | 1.30829i | −1.87939 | + | 0.684040i | 1.56822 | − | 4.74770i | −2.20498 | − | 1.85020i | −7.83152 | − | 4.52153i | 1.41421 | + | 2.44949i | −0.843479 | + | 4.78361i | −6.99738 | − | 1.01818i |
29.8 | −0.245576 | − | 1.39273i | 2.03549 | − | 1.70798i | −1.87939 | + | 0.684040i | 1.01591 | + | 4.89571i | −2.87862 | − | 2.41545i | 10.4469 | + | 6.03154i | 1.41421 | + | 2.44949i | −0.336806 | + | 1.91012i | 6.56891 | − | 2.61715i |
29.9 | −0.245576 | − | 1.39273i | 3.34876 | − | 2.80994i | −1.87939 | + | 0.684040i | −4.92535 | + | 0.860784i | −4.73586 | − | 3.97386i | −1.74818 | − | 1.00931i | 1.41421 | + | 2.44949i | 1.75558 | − | 9.95640i | 2.40838 | + | 6.64828i |
29.10 | −0.245576 | − | 1.39273i | 3.84296 | − | 3.22462i | −1.87939 | + | 0.684040i | 2.57704 | − | 4.28473i | −5.43476 | − | 4.56031i | 6.84923 | + | 3.95441i | 1.41421 | + | 2.44949i | 2.80729 | − | 15.9209i | −6.60032 | − | 2.53689i |
29.11 | 0.245576 | + | 1.39273i | −3.84296 | + | 3.22462i | −1.87939 | + | 0.684040i | −0.780045 | + | 4.93878i | −5.43476 | − | 4.56031i | −6.84923 | − | 3.95441i | −1.41421 | − | 2.44949i | 2.80729 | − | 15.9209i | −7.06994 | + | 0.126453i |
29.12 | 0.245576 | + | 1.39273i | −3.34876 | + | 2.80994i | −1.87939 | + | 0.684040i | −3.21973 | − | 3.82535i | −4.73586 | − | 3.97386i | 1.74818 | + | 1.00931i | −1.41421 | − | 2.44949i | 1.75558 | − | 9.95640i | 4.53699 | − | 5.42363i |
29.13 | 0.245576 | + | 1.39273i | −2.03549 | + | 1.70798i | −1.87939 | + | 0.684040i | 3.92513 | − | 3.09732i | −2.87862 | − | 2.41545i | −10.4469 | − | 6.03154i | −1.41421 | − | 2.44949i | −0.336806 | + | 1.91012i | 5.27764 | + | 4.70601i |
29.14 | 0.245576 | + | 1.39273i | −1.55916 | + | 1.30829i | −1.87939 | + | 0.684040i | −1.85044 | + | 4.64498i | −2.20498 | − | 1.85020i | 7.83152 | + | 4.52153i | −1.41421 | − | 2.44949i | −0.843479 | + | 4.78361i | −6.92362 | − | 1.43647i |
29.15 | 0.245576 | + | 1.39273i | −0.718479 | + | 0.602876i | −1.87939 | + | 0.684040i | 0.905861 | − | 4.91726i | −1.01608 | − | 0.852595i | 5.60642 | + | 3.23687i | −1.41421 | − | 2.44949i | −1.41008 | + | 7.99696i | 7.07086 | + | 0.0540596i |
29.16 | 0.245576 | + | 1.39273i | 0.344931 | − | 0.289432i | −1.87939 | + | 0.684040i | 3.60351 | + | 3.46623i | 0.487806 | + | 0.409318i | −3.92642 | − | 2.26692i | −1.41421 | − | 2.44949i | −1.52763 | + | 8.66360i | −3.94258 | + | 5.86993i |
29.17 | 0.245576 | + | 1.39273i | 1.00496 | − | 0.843264i | −1.87939 | + | 0.684040i | −4.88433 | − | 1.06926i | 1.42123 | + | 1.19256i | −5.78989 | − | 3.34280i | −1.41421 | − | 2.44949i | −1.26398 | + | 7.16837i | 0.289722 | − | 7.06513i |
29.18 | 0.245576 | + | 1.39273i | 2.27829 | − | 1.91171i | −1.87939 | + | 0.684040i | 4.99661 | + | 0.184101i | 3.22199 | + | 2.70357i | 5.25836 | + | 3.03592i | −1.41421 | − | 2.44949i | −0.0268715 | + | 0.152396i | 0.970642 | + | 7.00413i |
29.19 | 0.245576 | + | 1.39273i | 3.88588 | − | 3.26064i | −1.87939 | + | 0.684040i | −0.926396 | − | 4.91343i | 5.49546 | + | 4.61124i | −3.11910 | − | 1.80081i | −1.41421 | − | 2.44949i | 2.90545 | − | 16.4776i | 6.61557 | − | 2.49684i |
29.20 | 0.245576 | + | 1.39273i | 3.99079 | − | 3.34867i | −1.87939 | + | 0.684040i | −0.830467 | + | 4.93055i | 5.64382 | + | 4.73573i | 8.01154 | + | 4.62547i | −1.41421 | − | 2.44949i | 3.14997 | − | 17.8644i | −7.07086 | + | 0.0542075i |
See next 80 embeddings (of 120 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
19.f | odd | 18 | 1 | inner |
95.o | odd | 18 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 190.3.o.a | ✓ | 120 |
5.b | even | 2 | 1 | inner | 190.3.o.a | ✓ | 120 |
19.f | odd | 18 | 1 | inner | 190.3.o.a | ✓ | 120 |
95.o | odd | 18 | 1 | inner | 190.3.o.a | ✓ | 120 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
190.3.o.a | ✓ | 120 | 1.a | even | 1 | 1 | trivial |
190.3.o.a | ✓ | 120 | 5.b | even | 2 | 1 | inner |
190.3.o.a | ✓ | 120 | 19.f | odd | 18 | 1 | inner |
190.3.o.a | ✓ | 120 | 95.o | odd | 18 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(190, [\chi])\).