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Properties

Label 1175.4.a.i
Level $1175$
Weight $4$
Character orbit 1175.a
Self dual yes
Analytic conductor $69.327$
Analytic rank $0$
Dimension $28$
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: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - q^{2} - 7 q^{3} + 137 q^{4} + 34 q^{6} - 6 q^{7} + 18 q^{8} + 327 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - q^{2} - 7 q^{3} + 137 q^{4} + 34 q^{6} - 6 q^{7} + 18 q^{8} + 327 q^{9} + 101 q^{11} - 144 q^{12} + 84 q^{13} + 378 q^{14} + 681 q^{16} - 245 q^{17} + 181 q^{18} + 417 q^{19} + 334 q^{21} - 236 q^{22} + 80 q^{23} + 1057 q^{24} + 115 q^{26} - 229 q^{27} + 420 q^{28} + 376 q^{29} + 354 q^{31} - 507 q^{32} + 629 q^{33} + 628 q^{34} + 1539 q^{36} + 282 q^{37} + 413 q^{38} + 766 q^{39} + 885 q^{41} - 404 q^{42} + 62 q^{43} + 833 q^{44} + 1412 q^{46} - 1316 q^{47} - 1008 q^{48} + 2736 q^{49} + 2576 q^{51} + 806 q^{52} - 916 q^{53} + 1141 q^{54} + 4043 q^{56} + 2041 q^{57} - 1151 q^{58} + 516 q^{59} + 2190 q^{61} + 2516 q^{62} - 3571 q^{63} + 3408 q^{64} + 2949 q^{66} + 1147 q^{67} - 3052 q^{68} + 12 q^{69} + 2298 q^{71} + 2730 q^{72} - 17 q^{73} - 123 q^{74} + 5038 q^{76} + 3046 q^{77} - 2589 q^{78} + 2404 q^{79} + 8104 q^{81} + 1847 q^{82} - 5370 q^{83} + 2964 q^{84} + 2539 q^{86} + 4884 q^{87} - 4087 q^{88} + 2471 q^{89} + 4234 q^{91} + 4701 q^{92} - 3550 q^{93} + 47 q^{94} + 5840 q^{96} - 1636 q^{97} - 4348 q^{98} + 2924 q^{99}+O(q^{100}) \) 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 −5.65107 2.52195 23.9346 0 −14.2517 −13.1859 −90.0476 −20.6398 0
1.2 −5.37589 −6.60792 20.9002 0 35.5235 16.3170 −69.3501 16.6646 0
1.3 −4.84369 −8.92853 15.4613 0 43.2470 −35.0037 −36.1403 52.7186 0
1.4 −4.50721 3.59925 12.3149 0 −16.2226 35.5777 −19.4482 −14.0454 0
1.5 −4.35984 −7.60951 11.0082 0 33.1762 −8.36642 −13.1154 30.9046 0
1.6 −3.99349 1.66647 7.94796 0 −6.65502 −33.8463 0.207819 −24.2229 0
1.7 −3.49430 6.29466 4.21015 0 −21.9954 −17.3036 13.2429 12.6227 0
1.8 −2.92171 9.24059 0.536363 0 −26.9983 6.81095 21.8065 58.3884 0
1.9 −2.80229 −5.46778 −0.147176 0 15.3223 −1.86337 22.8307 2.89666 0
1.10 −2.35984 0.348519 −2.43116 0 −0.822449 25.9169 24.6159 −26.8785 0
1.11 −2.30757 4.51940 −2.67514 0 −10.4288 −5.62388 24.6336 −6.57499 0
1.12 −0.867849 −6.84404 −7.24684 0 5.93959 −1.90594 13.2319 19.8408 0
1.13 −0.794183 −2.11508 −7.36927 0 1.67976 31.6824 12.2060 −22.5264 0
1.14 −0.682908 10.1174 −7.53364 0 −6.90927 −29.8531 10.6080 75.3622 0
1.15 0.0928401 −10.1454 −7.99138 0 −0.941896 −16.6347 −1.48464 75.9282 0
1.16 0.453461 −1.33370 −7.79437 0 −0.604780 −5.57476 −7.16213 −25.2213 0
1.17 1.63938 7.85452 −5.31242 0 12.8766 26.3624 −21.8242 34.6934 0
1.18 1.65312 0.653068 −5.26721 0 1.07960 −23.9325 −21.9322 −26.5735 0
1.19 1.75741 −3.23822 −4.91150 0 −5.69090 15.1397 −22.6908 −16.5139 0
1.20 2.23851 3.32856 −2.98907 0 7.45101 0.815970 −24.5991 −15.9207 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
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.i ✓ 28
5.b even 2 1 1175.4.a.j yes 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1175.4.a.i ✓ 28 1.a even 1 1 trivial
1175.4.a.j yes 28 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{28} + T_{2}^{27} - 180 T_{2}^{26} - 181 T_{2}^{25} + 14311 T_{2}^{24} + 14542 T_{2}^{23} + \cdots + 60735543552 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1175))\). Copy content Toggle raw display