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Properties

Label 1175.4.a.l
Level $1175$
Weight $4$
Character orbit 1175.a
Self dual yes
Analytic conductor $69.327$
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] = [1175,4,Mod(1,1175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1175, 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("1175.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1175.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: \(69.3272442567\)
Analytic rank: \(0\)
Dimension: \(35\)
Twist minimal: no (minimal twist has level 235)
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.

\(\operatorname{Tr}(f)(q) = \) \( 35 q + 8 q^{2} + 12 q^{3} + 144 q^{4} + 12 q^{6} + 84 q^{7} + 96 q^{8} + 333 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 35 q + 8 q^{2} + 12 q^{3} + 144 q^{4} + 12 q^{6} + 84 q^{7} + 96 q^{8} + 333 q^{9} + 144 q^{12} + 294 q^{13} + 4 q^{14} + 580 q^{16} + 272 q^{17} + 1230 q^{18} - 96 q^{19} + 12 q^{21} + 484 q^{22} + 304 q^{23} - 54 q^{24} - 218 q^{26} + 432 q^{27} + 1350 q^{28} - 334 q^{29} - 248 q^{31} + 896 q^{32} + 1252 q^{33} + 148 q^{34} + 1836 q^{36} + 1480 q^{37} + 596 q^{38} - 332 q^{39} - 410 q^{41} + 672 q^{42} + 1506 q^{43} + 88 q^{44} - 456 q^{46} + 1645 q^{47} + 1298 q^{48} + 1459 q^{49} - 332 q^{51} + 3144 q^{52} + 1224 q^{53} + 524 q^{54} - 34 q^{56} + 4274 q^{57} + 1774 q^{58} - 86 q^{59} + 528 q^{61} + 2256 q^{62} + 1916 q^{63} + 2668 q^{64} + 1296 q^{66} + 4024 q^{67} + 286 q^{68} - 176 q^{69} + 556 q^{71} + 11280 q^{72} + 4584 q^{73} + 438 q^{74} - 3026 q^{76} + 3624 q^{77} + 446 q^{78} + 48 q^{79} + 4139 q^{81} + 2488 q^{82} + 1228 q^{83} - 3376 q^{84} - 610 q^{86} + 4770 q^{87} + 4168 q^{88} + 794 q^{89} + 1096 q^{91} + 4128 q^{92} + 1420 q^{93} + 376 q^{94} - 1100 q^{96} + 10624 q^{97} + 296 q^{98} + 1000 q^{99}+O(q^{100}) \) 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 −5.55705 0.0161589 22.8809 0 −0.0897960 27.2136 −82.6937 −26.9997 0
1.2 −4.99879 7.24871 16.9879 0 −36.2348 19.9894 −44.9286 25.5438 0
1.3 −4.81096 2.86822 15.1454 0 −13.7989 −24.2361 −34.3761 −18.7733 0
1.4 −4.24561 −4.91930 10.0252 0 20.8855 27.1044 −8.59838 −2.80045 0
1.5 −4.20784 1.10225 9.70591 0 −4.63810 −18.4918 −7.17821 −25.7850 0
1.6 −4.19753 −6.05406 9.61922 0 25.4121 17.5988 −6.79671 9.65163 0
1.7 −3.90065 1.73807 7.21505 0 −6.77960 3.78305 3.06180 −23.9791 0
1.8 −3.60123 −4.76456 4.96886 0 17.1583 −0.147913 10.9158 −4.29895 0
1.9 −2.91402 8.67089 0.491508 0 −25.2671 −6.75637 21.8799 48.1844 0
1.10 −2.82759 −6.97266 −0.00472282 0 19.7158 −18.0025 22.6341 21.6180 0
1.11 −2.55996 4.50635 −1.44660 0 −11.5361 −23.1424 24.1829 −6.69277 0
1.12 −1.68002 −1.62440 −5.17753 0 2.72903 −9.93150 22.1385 −24.3613 0
1.13 −1.62142 7.96955 −5.37101 0 −12.9220 20.3599 21.6800 36.5137 0
1.14 −0.772753 −7.17477 −7.40285 0 5.54433 13.2370 11.9026 24.4774 0
1.15 −0.725419 3.91187 −7.47377 0 −2.83775 26.7142 11.2250 −11.6972 0
1.16 −0.578830 −6.79385 −7.66496 0 3.93249 4.45794 9.06735 19.1564 0
1.17 −0.222357 6.42947 −7.95056 0 −1.42964 −32.0730 3.54672 14.3381 0
1.18 −0.0409420 4.04064 −7.99832 0 −0.165432 27.7565 0.655003 −10.6732 0
1.19 0.382055 −3.53314 −7.85403 0 −1.34985 −1.05373 −6.05711 −14.5169 0
1.20 1.01592 −10.0080 −6.96791 0 −10.1673 −5.68252 −15.2062 73.1602 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
\(5\) \(-1\)
\(47\) \(-1\)

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 1175.4.a.l 35
5.b even 2 1 1175.4.a.k 35
5.c odd 4 2 235.4.c.a ✓ 70
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
235.4.c.a ✓ 70 5.c odd 4 2
1175.4.a.k 35 5.b even 2 1
1175.4.a.l 35 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{35} - 8 T_{2}^{34} - 180 T_{2}^{33} + 1536 T_{2}^{32} + 14327 T_{2}^{31} - 132792 T_{2}^{30} + \cdots - 1441952432128 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1175))\). Copy content Toggle raw display