↑

Properties

Label 275.2.bm.b
Level $275$
Weight $2$
Character orbit 275.bm
Analytic conductor $2.196$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [275,2,Mod(7,275)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(275, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([5, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("275.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.bm (of order \(20\), degree \(8\), 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: \(2.19588605559\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36} + 8 q^{37} - 10 q^{38} + 40 q^{41} + 10 q^{42} + 60 q^{46} + 28 q^{47} + 54 q^{48} + 20 q^{51} + 50 q^{52} + 24 q^{53} - 80 q^{56} - 30 q^{57} + 50 q^{58} - 60 q^{61} - 100 q^{62} + 30 q^{63} - 100 q^{66} + 8 q^{67} + 30 q^{68} + 24 q^{71} - 80 q^{72} - 50 q^{73} - 70 q^{77} - 60 q^{78} - 12 q^{81} + 10 q^{82} - 90 q^{83} + 100 q^{86} - 170 q^{88} + 20 q^{91} + 68 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 −1.50135 + 0.237790i 0.361933 + 0.710333i 0.295389 − 0.0959778i 0 −0.712297 − 0.980393i −0.170602 − 0.0869260i 2.28811 − 1.16585i 1.38978 − 1.91287i 0
7.2 −0.482327 + 0.0763931i −0.517260 − 1.01518i −1.67531 + 0.544341i 0 0.327041 + 0.450133i 2.59854 + 1.32402i 1.63669 − 0.833936i 1.00032 − 1.37683i 0
7.3 1.22307 − 0.193716i −1.15501 − 2.26684i −0.443732 + 0.144177i 0 −1.85178 − 2.54876i −3.09022 − 1.57455i −2.72149 + 1.38667i −2.04114 + 2.80938i 0
7.4 2.40264 − 0.380541i 0.271495 + 0.532840i 3.72576 − 1.21057i 0 0.855073 + 1.17691i −2.30033 − 1.17208i 4.15610 − 2.11764i 1.55315 − 2.13772i 0
18.1 −0.380541 − 2.40264i −0.532840 + 0.271495i −3.72576 + 1.21057i 0 0.855073 + 1.17691i −1.17208 + 2.30033i 2.11764 + 4.15610i −1.55315 + 2.13772i 0
18.2 −0.193716 − 1.22307i 2.26684 − 1.15501i 0.443732 − 0.144177i 0 −1.85178 − 2.54876i −1.57455 + 3.09022i −1.38667 − 2.72149i 2.04114 − 2.80938i 0
18.3 0.0763931 + 0.482327i 1.01518 − 0.517260i 1.67531 − 0.544341i 0 0.327041 + 0.450133i 1.32402 − 2.59854i 0.833936 + 1.63669i −1.00032 + 1.37683i 0
18.4 0.237790 + 1.50135i −0.710333 + 0.361933i −0.295389 + 0.0959778i 0 −0.712297 − 0.980393i −0.0869260 + 0.170602i 1.16585 + 2.28811i −1.38978 + 1.91287i 0
57.1 −0.665529 − 1.30617i 0.130227 − 0.822224i −0.0875924 + 0.120561i 0 −1.16064 + 0.377114i 4.16343 − 0.659422i −2.68004 − 0.424477i 2.19408 + 0.712899i 0
57.2 0.261423 + 0.513072i −0.120415 + 0.760272i 0.980670 − 1.34978i 0 −0.421554 + 0.136971i −1.17850 + 0.186656i 2.08639 + 0.330452i 2.28966 + 0.743954i 0
57.3 0.474334 + 0.930933i 0.440550 − 2.78152i 0.533928 − 0.734888i 0 2.79838 − 0.909249i 0.543058 − 0.0860119i 3.00128 + 0.475357i −4.68963 − 1.52375i 0
57.4 1.15100 + 2.25897i −0.313634 + 1.98021i −2.60258 + 3.58214i 0 −4.83422 + 1.57073i 1.78576 − 0.282837i −6.07934 − 0.962874i −0.969677 − 0.315067i 0
68.1 −1.30617 + 0.665529i 0.822224 + 0.130227i 0.0875924 − 0.120561i 0 −1.16064 + 0.377114i −0.659422 − 4.16343i 0.424477 − 2.68004i −2.19408 − 0.712899i 0
68.2 0.513072 − 0.261423i −0.760272 − 0.120415i −0.980670 + 1.34978i 0 −0.421554 + 0.136971i 0.186656 + 1.17850i −0.330452 + 2.08639i −2.28966 − 0.743954i 0
68.3 0.930933 − 0.474334i 2.78152 + 0.440550i −0.533928 + 0.734888i 0 2.79838 − 0.909249i −0.0860119 − 0.543058i −0.475357 + 3.00128i 4.68963 + 1.52375i 0
68.4 2.25897 − 1.15100i −1.98021 − 0.313634i 2.60258 − 3.58214i 0 −4.83422 + 1.57073i −0.282837 − 1.78576i 0.962874 − 6.07934i 0.969677 + 0.315067i 0
107.1 −0.380541 + 2.40264i −0.532840 − 0.271495i −3.72576 − 1.21057i 0 0.855073 − 1.17691i −1.17208 − 2.30033i 2.11764 − 4.15610i −1.55315 − 2.13772i 0
107.2 −0.193716 + 1.22307i 2.26684 + 1.15501i 0.443732 + 0.144177i 0 −1.85178 + 2.54876i −1.57455 − 3.09022i −1.38667 + 2.72149i 2.04114 + 2.80938i 0
107.3 0.0763931 − 0.482327i 1.01518 + 0.517260i 1.67531 + 0.544341i 0 0.327041 − 0.450133i 1.32402 + 2.59854i 0.833936 − 1.63669i −1.00032 − 1.37683i 0
107.4 0.237790 − 1.50135i −0.710333 − 0.361933i −0.295389 − 0.0959778i 0 −0.712297 + 0.980393i −0.0869260 − 0.170602i 1.16585 − 2.28811i −1.38978 − 1.91287i 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 7.4
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
11.d odd 10 1 inner
55.l even 20 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 275.2.bm.b 32
5.b even 2 1 55.2.l.a ✓ 32
5.c odd 4 1 55.2.l.a ✓ 32
5.c odd 4 1 inner 275.2.bm.b 32
11.d odd 10 1 inner 275.2.bm.b 32
15.d odd 2 1 495.2.bj.a 32
15.e even 4 1 495.2.bj.a 32
20.d odd 2 1 880.2.cm.a 32
20.e even 4 1 880.2.cm.a 32
55.d odd 2 1 605.2.m.e 32
55.e even 4 1 605.2.m.e 32
55.h odd 10 1 55.2.l.a ✓ 32
55.h odd 10 1 605.2.e.b 32
55.h odd 10 1 605.2.m.c 32
55.h odd 10 1 605.2.m.d 32
55.j even 10 1 605.2.e.b 32
55.j even 10 1 605.2.m.c 32
55.j even 10 1 605.2.m.d 32
55.j even 10 1 605.2.m.e 32
55.k odd 20 1 605.2.e.b 32
55.k odd 20 1 605.2.m.c 32
55.k odd 20 1 605.2.m.d 32
55.k odd 20 1 605.2.m.e 32
55.l even 20 1 55.2.l.a ✓ 32
55.l even 20 1 inner 275.2.bm.b 32
55.l even 20 1 605.2.e.b 32
55.l even 20 1 605.2.m.c 32
55.l even 20 1 605.2.m.d 32
165.r even 10 1 495.2.bj.a 32
165.u odd 20 1 495.2.bj.a 32
220.o even 10 1 880.2.cm.a 32
220.w odd 20 1 880.2.cm.a 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.2.l.a ✓ 32 5.b even 2 1
55.2.l.a ✓ 32 5.c odd 4 1
55.2.l.a ✓ 32 55.h odd 10 1
55.2.l.a ✓ 32 55.l even 20 1
275.2.bm.b 32 1.a even 1 1 trivial
275.2.bm.b 32 5.c odd 4 1 inner
275.2.bm.b 32 11.d odd 10 1 inner
275.2.bm.b 32 55.l even 20 1 inner
495.2.bj.a 32 15.d odd 2 1
495.2.bj.a 32 15.e even 4 1
495.2.bj.a 32 165.r even 10 1
495.2.bj.a 32 165.u odd 20 1
605.2.e.b 32 55.h odd 10 1
605.2.e.b 32 55.j even 10 1
605.2.e.b 32 55.k odd 20 1
605.2.e.b 32 55.l even 20 1
605.2.m.c 32 55.h odd 10 1
605.2.m.c 32 55.j even 10 1
605.2.m.c 32 55.k odd 20 1
605.2.m.c 32 55.l even 20 1
605.2.m.d 32 55.h odd 10 1
605.2.m.d 32 55.j even 10 1
605.2.m.d 32 55.k odd 20 1
605.2.m.d 32 55.l even 20 1
605.2.m.e 32 55.d odd 2 1
605.2.m.e 32 55.e even 4 1
605.2.m.e 32 55.j even 10 1
605.2.m.e 32 55.k odd 20 1
880.2.cm.a 32 20.d odd 2 1
880.2.cm.a 32 20.e even 4 1
880.2.cm.a 32 220.o even 10 1
880.2.cm.a 32 220.w odd 20 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{32} - 10 T_{2}^{31} + 50 T_{2}^{30} - 170 T_{2}^{29} + 430 T_{2}^{28} - 800 T_{2}^{27} + \cdots + 625 \) acting on \(S_{2}^{\mathrm{new}}(275, [\chi])\). Copy content Toggle raw display