Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(229,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.c (of order \(2\), degree \(1\), 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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
229.1 | − | 1.41421i | − | 5.45221i | −2.00000 | −3.90521 | + | 3.12239i | −7.71059 | 0.770899 | 2.82843i | −20.7266 | 4.41573 | + | 5.52280i | ||||||||||||
229.2 | − | 1.41421i | − | 5.45221i | −2.00000 | 3.90521 | − | 3.12239i | −7.71059 | −0.770899 | 2.82843i | −20.7266 | −4.41573 | − | 5.52280i | ||||||||||||
229.3 | − | 1.41421i | − | 2.29017i | −2.00000 | −2.28201 | − | 4.44887i | −3.23879 | −9.92340 | 2.82843i | 3.75511 | −6.29165 | + | 3.22725i | ||||||||||||
229.4 | − | 1.41421i | − | 2.29017i | −2.00000 | 2.28201 | + | 4.44887i | −3.23879 | 9.92340 | 2.82843i | 3.75511 | 6.29165 | − | 3.22725i | ||||||||||||
229.5 | − | 1.41421i | − | 0.894518i | −2.00000 | −3.14390 | + | 3.88792i | −1.26504 | −4.24317 | 2.82843i | 8.19984 | 5.49835 | + | 4.44614i | ||||||||||||
229.6 | − | 1.41421i | − | 0.894518i | −2.00000 | 3.14390 | − | 3.88792i | −1.26504 | 4.24317 | 2.82843i | 8.19984 | −5.49835 | − | 4.44614i | ||||||||||||
229.7 | − | 1.41421i | 1.47600i | −2.00000 | −4.75172 | + | 1.55601i | 2.08738 | 0.788814 | 2.82843i | 6.82142 | 2.20053 | + | 6.71994i | |||||||||||||
229.8 | − | 1.41421i | 1.47600i | −2.00000 | 4.75172 | − | 1.55601i | 2.08738 | −0.788814 | 2.82843i | 6.82142 | −2.20053 | − | 6.71994i | |||||||||||||
229.9 | − | 1.41421i | 3.00625i | −2.00000 | −3.95888 | − | 3.05405i | 4.25149 | 7.53698 | 2.82843i | −0.0375672 | −4.31908 | + | 5.59871i | |||||||||||||
229.10 | − | 1.41421i | 3.00625i | −2.00000 | 3.95888 | + | 3.05405i | 4.25149 | −7.53698 | 2.82843i | −0.0375672 | 4.31908 | − | 5.59871i | |||||||||||||
229.11 | − | 1.41421i | 5.56886i | −2.00000 | −0.637273 | + | 4.95922i | 7.87556 | 10.0249 | 2.82843i | −22.0122 | 7.01340 | + | 0.901240i | |||||||||||||
229.12 | − | 1.41421i | 5.56886i | −2.00000 | 0.637273 | − | 4.95922i | 7.87556 | −10.0249 | 2.82843i | −22.0122 | −7.01340 | − | 0.901240i | |||||||||||||
229.13 | 1.41421i | − | 5.56886i | −2.00000 | −0.637273 | − | 4.95922i | 7.87556 | 10.0249 | − | 2.82843i | −22.0122 | 7.01340 | − | 0.901240i | ||||||||||||
229.14 | 1.41421i | − | 5.56886i | −2.00000 | 0.637273 | + | 4.95922i | 7.87556 | −10.0249 | − | 2.82843i | −22.0122 | −7.01340 | + | 0.901240i | ||||||||||||
229.15 | 1.41421i | − | 3.00625i | −2.00000 | −3.95888 | + | 3.05405i | 4.25149 | 7.53698 | − | 2.82843i | −0.0375672 | −4.31908 | − | 5.59871i | ||||||||||||
229.16 | 1.41421i | − | 3.00625i | −2.00000 | 3.95888 | − | 3.05405i | 4.25149 | −7.53698 | − | 2.82843i | −0.0375672 | 4.31908 | + | 5.59871i | ||||||||||||
229.17 | 1.41421i | − | 1.47600i | −2.00000 | −4.75172 | − | 1.55601i | 2.08738 | 0.788814 | − | 2.82843i | 6.82142 | 2.20053 | − | 6.71994i | ||||||||||||
229.18 | 1.41421i | − | 1.47600i | −2.00000 | 4.75172 | + | 1.55601i | 2.08738 | −0.788814 | − | 2.82843i | 6.82142 | −2.20053 | + | 6.71994i | ||||||||||||
229.19 | 1.41421i | 0.894518i | −2.00000 | −3.14390 | − | 3.88792i | −1.26504 | −4.24317 | − | 2.82843i | 8.19984 | 5.49835 | − | 4.44614i | |||||||||||||
229.20 | 1.41421i | 0.894518i | −2.00000 | 3.14390 | + | 3.88792i | −1.26504 | 4.24317 | − | 2.82843i | 8.19984 | −5.49835 | + | 4.44614i | |||||||||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
23.b | odd | 2 | 1 | inner |
115.c | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 230.3.c.a | ✓ | 24 |
5.b | even | 2 | 1 | inner | 230.3.c.a | ✓ | 24 |
5.c | odd | 4 | 2 | 1150.3.d.e | 24 | ||
23.b | odd | 2 | 1 | inner | 230.3.c.a | ✓ | 24 |
115.c | odd | 2 | 1 | inner | 230.3.c.a | ✓ | 24 |
115.e | even | 4 | 2 | 1150.3.d.e | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
230.3.c.a | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
230.3.c.a | ✓ | 24 | 5.b | even | 2 | 1 | inner |
230.3.c.a | ✓ | 24 | 23.b | odd | 2 | 1 | inner |
230.3.c.a | ✓ | 24 | 115.c | odd | 2 | 1 | inner |
1150.3.d.e | 24 | 5.c | odd | 4 | 2 | ||
1150.3.d.e | 24 | 115.e | even | 4 | 2 |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(230, [\chi])\).