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Properties

Label 1175.4.a.k
Level $1175$
Weight $4$
Character orbit 1175.a
Self dual yes
Analytic conductor $69.327$
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] = [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: \(1\)
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 −5.44181 −9.61264 21.6133 0 52.3101 3.18981 −74.0808 65.4028 0
1.2 −5.41648 10.1007 21.3382 0 −54.7104 −23.8037 −72.2463 75.0246 0
1.3 −5.14712 0.847324 18.4929 0 −4.36128 2.35956 −54.0081 −26.2820 0
1.4 −5.10404 −6.67479 18.0513 0 34.0684 −24.0952 −51.3021 17.5528 0
1.5 −4.82737 −3.80919 15.3035 0 18.3884 −14.8996 −35.2567 −12.4901 0
1.6 −4.26255 5.84964 10.1694 0 −24.9344 0.396184 −9.24705 7.21834 0
1.7 −3.89635 6.76134 7.18157 0 −26.3446 33.3533 3.18889 18.7157 0
1.8 −3.78431 7.04312 6.32101 0 −26.6533 −15.0521 6.35384 22.6055 0
1.9 −3.69154 −9.25728 5.62745 0 34.1736 24.2439 8.75836 58.6972 0
1.10 −3.02390 −7.50502 1.14400 0 22.6945 −33.4031 20.7319 29.3254 0
1.11 −2.86481 −0.442669 0.207114 0 1.26816 22.5898 22.3251 −26.8040 0
1.12 −2.53923 2.09148 −1.55230 0 −5.31076 16.0004 24.2555 −22.6257 0
1.13 −2.23775 −9.94561 −2.99250 0 22.2557 −4.16733 24.5984 71.9152 0
1.14 −2.05829 1.38983 −3.76346 0 −2.86067 −30.0134 24.2126 −25.0684 0
1.15 −1.76945 −2.17884 −4.86904 0 3.85536 7.99843 22.7711 −22.2526 0
1.16 −1.01592 10.0080 −6.96791 0 −10.1673 5.68252 15.2062 73.1602 0
1.17 −0.382055 3.53314 −7.85403 0 −1.34985 1.05373 6.05711 −14.5169 0
1.18 0.0409420 −4.04064 −7.99832 0 −0.165432 −27.7565 −0.655003 −10.6732 0
1.19 0.222357 −6.42947 −7.95056 0 −1.42964 32.0730 −3.54672 14.3381 0
1.20 0.578830 6.79385 −7.66496 0 3.93249 −4.45794 −9.06735 19.1564 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.k 35
5.b even 2 1 1175.4.a.l 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 1.a even 1 1 trivial
1175.4.a.l 35 5.b even 2 1

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