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Properties

Label 1775.4.a.j
Level $1775$
Weight $4$
Character orbit 1775.a
Self dual yes
Analytic conductor $104.728$
Analytic rank $0$
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: \(0\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 35 q + 2 q^{2} + 5 q^{3} + 146 q^{4} + 8 q^{6} + 92 q^{7} + 24 q^{8} + 286 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 35 q + 2 q^{2} + 5 q^{3} + 146 q^{4} + 8 q^{6} + 92 q^{7} + 24 q^{8} + 286 q^{9} + 29 q^{11} + 60 q^{12} + 314 q^{13} - 48 q^{14} + 542 q^{16} + 265 q^{17} + 80 q^{18} + 149 q^{19} - 216 q^{21} + 893 q^{22} + 200 q^{23} + 100 q^{24} - 785 q^{26} + 665 q^{27} + 1267 q^{28} + 318 q^{29} - 156 q^{31} + 934 q^{32} + 1565 q^{33} + 1008 q^{34} - 686 q^{36} + 1342 q^{37} + 425 q^{38} + 322 q^{39} - 49 q^{41} + 1668 q^{42} + 792 q^{43} + 383 q^{44} - 406 q^{46} + 1104 q^{47} + 44 q^{48} + 1737 q^{49} - 123 q^{51} + 3195 q^{52} + 386 q^{53} + 1253 q^{54} - 403 q^{56} + 2451 q^{57} + 2067 q^{58} - 242 q^{59} + 286 q^{61} + 761 q^{62} + 2628 q^{63} + 2438 q^{64} - 1354 q^{66} + 1131 q^{67} + 2567 q^{68} - 668 q^{69} - 2485 q^{71} + 145 q^{72} + 6721 q^{73} - 2092 q^{74} + 499 q^{76} + 1588 q^{77} + 4749 q^{78} - 1660 q^{79} + 6823 q^{81} + 3461 q^{82} + 3881 q^{83} - 6139 q^{84} + 1532 q^{86} + 966 q^{87} + 7326 q^{88} - 1197 q^{89} + 4418 q^{91} + 4753 q^{92} + 4556 q^{93} - 3211 q^{94} + 657 q^{96} + 6116 q^{97} + 3902 q^{98} - 4872 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.61602 −0.117117 23.5397 0 0.657730 18.7860 −87.2711 −26.9863 0
1.2 −4.91345 −1.24043 16.1420 0 6.09477 30.9682 −40.0052 −25.4613 0
1.3 −4.76377 −0.0632141 14.6935 0 0.301137 −18.0140 −31.8861 −26.9960 0
1.4 −4.64808 8.64711 13.6047 0 −40.1925 −12.2813 −26.0509 47.7726 0
1.5 −4.33554 −9.45903 10.7969 0 41.0100 28.9189 −12.1261 62.4732 0
1.6 −4.31605 3.90870 10.6283 0 −16.8701 −13.1727 −11.3438 −11.7221 0
1.7 −4.03459 −5.52840 8.27794 0 22.3048 12.6211 −1.12136 3.56322 0
1.8 −3.75605 5.84277 6.10793 0 −21.9458 23.7239 7.10671 7.13799 0
1.9 −3.68501 −5.70707 5.57933 0 21.0306 −18.2190 8.92021 5.57061 0
1.10 −3.08479 8.82515 1.51596 0 −27.2238 −25.5192 20.0019 50.8832 0
1.11 −2.83705 −5.06157 0.0488675 0 14.3599 −0.724659 22.5578 −1.38055 0
1.12 −1.86637 8.65835 −4.51665 0 −16.1597 24.7813 23.3607 47.9670 0
1.13 −1.65442 1.70193 −5.26288 0 −2.81572 1.45858 21.9424 −24.1034 0
1.14 −1.04488 −1.49381 −6.90823 0 1.56084 −8.21528 15.5773 −24.7685 0
1.15 −0.938527 2.15825 −7.11917 0 −2.02558 8.56888 14.1897 −22.3420 0
1.16 −0.617242 −7.35156 −7.61901 0 4.53769 11.7117 9.64071 27.0454 0
1.17 −0.467307 −8.97143 −7.78162 0 4.19241 −8.94270 7.37487 53.4866 0
1.18 −0.0928775 −4.41619 −7.99137 0 0.410165 −22.8226 1.48524 −7.49728 0
1.19 0.0409591 2.18890 −7.99832 0 0.0896553 32.0295 −0.655277 −22.2087 0
1.20 1.08161 9.94150 −6.83012 0 10.7528 15.6762 −16.0404 71.8334 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.j yes 35
5.b even 2 1 1775.4.a.i ✓ 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1775.4.a.i ✓ 35 5.b even 2 1
1775.4.a.j yes 35 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{35} - 2 T_{2}^{34} - 211 T_{2}^{33} + 406 T_{2}^{32} + 20165 T_{2}^{31} - 37352 T_{2}^{30} + \cdots - 1095257518080 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1775))\). Copy content Toggle raw display