Properties

Label 1775.4.a.h
Level $1775$
Weight $4$
Character orbit 1775.a
Self dual yes
Analytic conductor $104.728$
Analytic rank $1$
Dimension $35$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1775,4,Mod(1,1775)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1775, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1775.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1775 = 5^{2} \cdot 71 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1775.a (trivial)

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: yes
Analytic conductor: \(104.728390260\)
Analytic rank: \(1\)
Dimension: \(35\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9} + 29 q^{11} - 228 q^{12} - 206 q^{13} - 48 q^{14} + 542 q^{16} - 347 q^{17} - 280 q^{18} - 59 q^{19} + 284 q^{21} - 605 q^{22} - 168 q^{23} + 100 q^{24} + 655 q^{26} - 727 q^{27} - 749 q^{28} - 522 q^{29} + 84 q^{31} - 1522 q^{32} - 547 q^{33} - 324 q^{34} + 2114 q^{36} - 706 q^{37} - 487 q^{38} - 574 q^{39} + 311 q^{41} - 1602 q^{42} - 928 q^{43} - 1129 q^{44} + 144 q^{46} - 744 q^{47} - 2644 q^{48} + 1649 q^{49} + 277 q^{51} - 2727 q^{52} - 886 q^{53} - 923 q^{54} + 947 q^{56} - 2501 q^{57} - 1181 q^{58} - 434 q^{59} + 466 q^{61} - 1727 q^{62} - 1908 q^{63} + 2102 q^{64} - 884 q^{66} - 2425 q^{67} - 2329 q^{68} - 716 q^{69} + 2485 q^{71} - 4079 q^{72} - 5803 q^{73} - 412 q^{74} - 3109 q^{76} - 732 q^{77} - 2691 q^{78} + 1024 q^{79} + 7 q^{81} - 1325 q^{82} - 4927 q^{83} + 3889 q^{84} - 2716 q^{86} - 2634 q^{87} - 7122 q^{88} + 3279 q^{89} - 3782 q^{91} + 3025 q^{92} - 5256 q^{93} + 1485 q^{94} - 3043 q^{96} - 8548 q^{97} - 5578 q^{98} + 9008 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.43552 −6.81462 21.5448 0 37.0410 −19.9909 −73.6232 19.4390 0
1.2 −5.35883 6.20090 20.7170 0 −33.2296 −14.7177 −68.1483 11.4512 0
1.3 −5.04000 7.78107 17.4016 0 −39.2166 23.3422 −47.3838 33.5450 0
1.4 −4.93007 −6.89641 16.3056 0 33.9998 17.8269 −40.9471 20.5604 0
1.5 −4.92747 −2.13307 16.2800 0 10.5107 −13.5385 −40.7995 −22.4500 0
1.6 −4.88806 −9.25374 15.8931 0 45.2328 −14.1247 −38.5818 58.6317 0
1.7 −3.68922 0.964798 5.61037 0 −3.55935 15.6323 8.81589 −26.0692 0
1.8 −3.62886 4.19786 5.16860 0 −15.2334 14.0872 10.2747 −9.37797 0
1.9 −3.21242 0.727523 2.31967 0 −2.33711 −34.8359 18.2476 −26.4707 0
1.10 −2.72200 −8.90621 −0.590701 0 24.2427 −22.0247 23.3839 52.3205 0
1.11 −2.69853 −3.56505 −0.717958 0 9.62039 12.6141 23.5256 −14.2904 0
1.12 −2.46188 9.46716 −1.93913 0 −23.3070 10.9485 24.4690 62.6271 0
1.13 −2.34854 4.37444 −2.48434 0 −10.2736 −7.56358 24.6229 −7.86427 0
1.14 −1.72350 0.574848 −5.02956 0 −0.990749 −31.3635 22.4564 −26.6695 0
1.15 −1.67295 −2.56658 −5.20125 0 4.29375 33.3152 22.0850 −20.4127 0
1.16 −1.33849 −9.01832 −6.20846 0 12.0709 28.5031 19.0178 54.3300 0
1.17 −0.817514 6.54962 −7.33167 0 −5.35441 −5.21825 12.5339 15.8976 0
1.18 −0.326193 −3.04731 −7.89360 0 0.994014 −25.8341 5.18439 −17.7139 0
1.19 −0.0851169 7.65756 −7.99276 0 −0.651788 −21.8205 1.36125 31.6382 0
1.20 0.730043 −6.29077 −7.46704 0 −4.59253 0.329954 −11.2916 12.5738 0
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(71\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1775.4.a.h 35
5.b even 2 1 1775.4.a.k yes 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1775.4.a.h 35 1.a even 1 1 trivial
1775.4.a.k yes 35 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{35} + 6 T_{2}^{34} - 195 T_{2}^{33} - 1186 T_{2}^{32} + 17109 T_{2}^{31} + 105944 T_{2}^{30} - 892075 T_{2}^{29} - 5659327 T_{2}^{28} + 30743515 T_{2}^{27} + 201621760 T_{2}^{26} + \cdots + 38781671215104 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1775))\). Copy content Toggle raw display