Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,5,Mod(91,230)]
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([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.91");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.d (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: | \(23.7750915093\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-expansion
The algebraic \(q\)-expansion of this newform has not been computed, 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
91.1 | −2.82843 | −5.93906 | 8.00000 | − | 11.1803i | 16.7982 | − | 85.3294i | −22.6274 | −45.7275 | 31.6228i | ||||||||||||||||
91.2 | −2.82843 | −11.3966 | 8.00000 | 11.1803i | 32.2344 | − | 85.1794i | −22.6274 | 48.8818 | − | 31.6228i | ||||||||||||||||
91.3 | −2.82843 | 7.33271 | 8.00000 | 11.1803i | −20.7400 | − | 75.6542i | −22.6274 | −27.2314 | − | 31.6228i | ||||||||||||||||
91.4 | −2.82843 | 15.6893 | 8.00000 | 11.1803i | −44.3761 | 65.6030i | −22.6274 | 165.154 | − | 31.6228i | |||||||||||||||||
91.5 | −2.82843 | −5.71864 | 8.00000 | − | 11.1803i | 16.1747 | − | 36.1607i | −22.6274 | −48.2972 | 31.6228i | ||||||||||||||||
91.6 | −2.82843 | −14.3217 | 8.00000 | 11.1803i | 40.5079 | 16.7293i | −22.6274 | 124.111 | − | 31.6228i | |||||||||||||||||
91.7 | −2.82843 | 0.828614 | 8.00000 | − | 11.1803i | −2.34367 | 16.9191i | −22.6274 | −80.3134 | 31.6228i | |||||||||||||||||
91.8 | −2.82843 | 7.86848 | 8.00000 | − | 11.1803i | −22.2554 | − | 5.16947i | −22.6274 | −19.0870 | 31.6228i | ||||||||||||||||
91.9 | −2.82843 | 7.86848 | 8.00000 | 11.1803i | −22.2554 | 5.16947i | −22.6274 | −19.0870 | − | 31.6228i | |||||||||||||||||
91.10 | −2.82843 | 0.828614 | 8.00000 | 11.1803i | −2.34367 | − | 16.9191i | −22.6274 | −80.3134 | − | 31.6228i | ||||||||||||||||
91.11 | −2.82843 | −14.3217 | 8.00000 | − | 11.1803i | 40.5079 | − | 16.7293i | −22.6274 | 124.111 | 31.6228i | ||||||||||||||||
91.12 | −2.82843 | −5.71864 | 8.00000 | 11.1803i | 16.1747 | 36.1607i | −22.6274 | −48.2972 | − | 31.6228i | |||||||||||||||||
91.13 | −2.82843 | 15.6893 | 8.00000 | − | 11.1803i | −44.3761 | − | 65.6030i | −22.6274 | 165.154 | 31.6228i | ||||||||||||||||
91.14 | −2.82843 | 7.33271 | 8.00000 | − | 11.1803i | −20.7400 | 75.6542i | −22.6274 | −27.2314 | 31.6228i | |||||||||||||||||
91.15 | −2.82843 | −11.3966 | 8.00000 | − | 11.1803i | 32.2344 | 85.1794i | −22.6274 | 48.8818 | 31.6228i | |||||||||||||||||
91.16 | −2.82843 | −5.93906 | 8.00000 | 11.1803i | 16.7982 | 85.3294i | −22.6274 | −45.7275 | − | 31.6228i | |||||||||||||||||
91.17 | 2.82843 | 17.4598 | 8.00000 | 11.1803i | 49.3837 | − | 69.3646i | 22.6274 | 223.844 | 31.6228i | |||||||||||||||||
91.18 | 2.82843 | −0.0560696 | 8.00000 | − | 11.1803i | −0.158589 | 58.4359i | 22.6274 | −80.9969 | − | 31.6228i | ||||||||||||||||
91.19 | 2.82843 | 11.3074 | 8.00000 | − | 11.1803i | 31.9821 | − | 52.5241i | 22.6274 | 46.8567 | − | 31.6228i | |||||||||||||||
91.20 | 2.82843 | −2.20532 | 8.00000 | − | 11.1803i | −6.23758 | − | 53.7736i | 22.6274 | −76.1366 | − | 31.6228i | |||||||||||||||
See all 32 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
23.b | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 230.5.d.a | ✓ | 32 |
23.b | odd | 2 | 1 | inner | 230.5.d.a | ✓ | 32 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
230.5.d.a | ✓ | 32 | 1.a | even | 1 | 1 | trivial |
230.5.d.a | ✓ | 32 | 23.b | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(230, [\chi])\).