Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(19,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 15]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.i (of order \(22\), degree \(10\), 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: | \(240\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{22})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{22}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
19.1 | −1.28641 | + | 0.587486i | −1.51772 | − | 5.16888i | 1.30972 | − | 1.51150i | −4.19163 | + | 2.72584i | 4.98906 | + | 5.75768i | 0.512235 | + | 3.56267i | −0.796860 | + | 2.71386i | −16.8426 | + | 10.8241i | 3.79078 | − | 5.96909i |
19.2 | −1.28641 | + | 0.587486i | −1.02272 | − | 3.48306i | 1.30972 | − | 1.51150i | −2.37251 | − | 4.40127i | 3.36189 | + | 3.87983i | −1.08475 | − | 7.54462i | −0.796860 | + | 2.71386i | −3.51448 | + | 2.25862i | 5.63771 | + | 4.26804i |
19.3 | −1.28641 | + | 0.587486i | −0.859820 | − | 2.92828i | 1.30972 | − | 1.51150i | 2.44584 | − | 4.36095i | 2.82640 | + | 3.26184i | 1.96650 | + | 13.6773i | −0.796860 | + | 2.71386i | −0.264236 | + | 0.169814i | −0.584368 | + | 7.04688i |
19.4 | −1.28641 | + | 0.587486i | −0.810314 | − | 2.75968i | 1.30972 | − | 1.51150i | 4.95827 | − | 0.644601i | 2.66367 | + | 3.07404i | −0.976678 | − | 6.79294i | −0.796860 | + | 2.71386i | 0.612076 | − | 0.393358i | −5.99970 | + | 3.74214i |
19.5 | −1.28641 | + | 0.587486i | −0.424421 | − | 1.44544i | 1.30972 | − | 1.51150i | 3.70278 | + | 3.35997i | 1.39516 | + | 1.61010i | 1.33136 | + | 9.25983i | −0.796860 | + | 2.71386i | 5.66211 | − | 3.63882i | −6.73725 | − | 2.14698i |
19.6 | −1.28641 | + | 0.587486i | −0.00972304 | − | 0.0331137i | 1.30972 | − | 1.51150i | −4.99585 | + | 0.203788i | 0.0319617 | + | 0.0368857i | 0.869641 | + | 6.04849i | −0.796860 | + | 2.71386i | 7.57028 | − | 4.86512i | 6.30700 | − | 3.19714i |
19.7 | −1.28641 | + | 0.587486i | 0.271363 | + | 0.924178i | 1.30972 | − | 1.51150i | −2.58664 | + | 4.27894i | −0.892026 | − | 1.02945i | −1.64158 | − | 11.4174i | −0.796860 | + | 2.71386i | 6.79082 | − | 4.36419i | 0.813673 | − | 7.02410i |
19.8 | −1.28641 | + | 0.587486i | 0.540708 | + | 1.84148i | 1.30972 | − | 1.51150i | 4.67844 | + | 1.76413i | −1.77742 | − | 2.05125i | −0.0656966 | − | 0.456930i | −0.796860 | + | 2.71386i | 4.47258 | − | 2.87436i | −7.05482 | + | 0.479116i |
19.9 | −1.28641 | + | 0.587486i | 0.576935 | + | 1.96486i | 1.30972 | − | 1.51150i | 1.83597 | − | 4.65072i | −1.89650 | − | 2.18868i | −0.457318 | − | 3.18071i | −0.796860 | + | 2.71386i | 4.04347 | − | 2.59858i | 0.370417 | + | 7.06136i |
19.10 | −1.28641 | + | 0.587486i | 0.725559 | + | 2.47103i | 1.30972 | − | 1.51150i | −2.80253 | − | 4.14075i | −2.38506 | − | 2.75251i | 0.102488 | + | 0.712820i | −0.796860 | + | 2.71386i | 1.99174 | − | 1.28002i | 6.03785 | + | 3.68027i |
19.11 | −1.28641 | + | 0.587486i | 1.23261 | + | 4.19789i | 1.30972 | − | 1.51150i | −2.21082 | + | 4.48467i | −4.05185 | − | 4.67609i | 0.828200 | + | 5.76026i | −0.796860 | + | 2.71386i | −8.53169 | + | 5.48298i | 0.209350 | − | 7.06797i |
19.12 | −1.28641 | + | 0.587486i | 1.62857 | + | 5.54639i | 1.30972 | − | 1.51150i | 4.18474 | − | 2.73642i | −5.35343 | − | 6.17819i | 0.543186 | + | 3.77794i | −0.796860 | + | 2.71386i | −20.5389 | + | 13.1996i | −3.77570 | + | 5.97864i |
19.13 | 1.28641 | − | 0.587486i | −1.62857 | − | 5.54639i | 1.30972 | − | 1.51150i | 0.750729 | − | 4.94332i | −5.35343 | − | 6.17819i | −0.543186 | − | 3.77794i | 0.796860 | − | 2.71386i | −20.5389 | + | 13.1996i | −1.93838 | − | 6.80020i |
19.14 | 1.28641 | − | 0.587486i | −1.23261 | − | 4.19789i | 1.30972 | − | 1.51150i | −3.16099 | + | 3.87403i | −4.05185 | − | 4.67609i | −0.828200 | − | 5.76026i | 0.796860 | − | 2.71386i | −8.53169 | + | 5.48298i | −1.79041 | + | 6.84065i |
19.15 | 1.28641 | − | 0.587486i | −0.725559 | − | 2.47103i | 1.30972 | − | 1.51150i | 4.93077 | + | 0.829144i | −2.38506 | − | 2.75251i | −0.102488 | − | 0.712820i | 0.796860 | − | 2.71386i | 1.99174 | − | 1.28002i | 6.83012 | − | 1.83014i |
19.16 | 1.28641 | − | 0.587486i | −0.576935 | − | 1.96486i | 1.30972 | − | 1.51150i | 3.46776 | − | 3.60204i | −1.89650 | − | 2.18868i | 0.457318 | + | 3.18071i | 0.796860 | − | 2.71386i | 4.04347 | − | 2.59858i | 2.34483 | − | 6.67097i |
19.17 | 1.28641 | − | 0.587486i | −0.540708 | − | 1.84148i | 1.30972 | − | 1.51150i | −3.54821 | − | 3.52282i | −1.77742 | − | 2.05125i | 0.0656966 | + | 0.456930i | 0.796860 | − | 2.71386i | 4.47258 | − | 2.87436i | −6.63406 | − | 2.44728i |
19.18 | 1.28641 | − | 0.587486i | −0.271363 | − | 0.924178i | 1.30972 | − | 1.51150i | −2.81773 | + | 4.13042i | −0.892026 | − | 1.02945i | 1.64158 | + | 11.4174i | 0.796860 | − | 2.71386i | 6.79082 | − | 4.36419i | −1.19820 | + | 6.96881i |
19.19 | 1.28641 | − | 0.587486i | 0.00972304 | + | 0.0331137i | 1.30972 | − | 1.51150i | 1.88998 | + | 4.62904i | 0.0319617 | + | 0.0368857i | −0.869641 | − | 6.04849i | 0.796860 | − | 2.71386i | 7.57028 | − | 4.86512i | 5.15079 | + | 4.84452i |
19.20 | 1.28641 | − | 0.587486i | 0.424421 | + | 1.44544i | 1.30972 | − | 1.51150i | −4.59453 | − | 1.97239i | 1.39516 | + | 1.61010i | −1.33136 | − | 9.25983i | 0.796860 | − | 2.71386i | 5.66211 | − | 3.63882i | −7.06921 | + | 0.161910i |
See next 80 embeddings (of 240 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
23.d | odd | 22 | 1 | inner |
115.i | odd | 22 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 230.3.i.a | ✓ | 240 |
5.b | even | 2 | 1 | inner | 230.3.i.a | ✓ | 240 |
23.d | odd | 22 | 1 | inner | 230.3.i.a | ✓ | 240 |
115.i | odd | 22 | 1 | inner | 230.3.i.a | ✓ | 240 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
230.3.i.a | ✓ | 240 | 1.a | even | 1 | 1 | trivial |
230.3.i.a | ✓ | 240 | 5.b | even | 2 | 1 | inner |
230.3.i.a | ✓ | 240 | 23.d | odd | 22 | 1 | inner |
230.3.i.a | ✓ | 240 | 115.i | odd | 22 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(230, [\chi])\).