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Properties

Label 633.4.a.d
Level $633$
Weight $4$
Character orbit 633.a
Self dual yes
Analytic conductor $37.348$
Analytic rank $0$
Dimension $26$
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] = [633,4,Mod(1,633)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(633, 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("633.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 633 = 3 \cdot 211 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 633.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: \(37.3482090336\)
Analytic rank: \(0\)
Dimension: \(26\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q + 6 q^{2} - 78 q^{3} + 108 q^{4} + 25 q^{5} - 18 q^{6} + 50 q^{7} + 57 q^{8} + 234 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q + 6 q^{2} - 78 q^{3} + 108 q^{4} + 25 q^{5} - 18 q^{6} + 50 q^{7} + 57 q^{8} + 234 q^{9} - 32 q^{10} + 73 q^{11} - 324 q^{12} - 61 q^{13} + 243 q^{14} - 75 q^{15} + 440 q^{16} + 96 q^{17} + 54 q^{18} + 71 q^{19} + 277 q^{20} - 150 q^{21} + 206 q^{22} + 678 q^{23} - 171 q^{24} + 597 q^{25} + 335 q^{26} - 702 q^{27} + 354 q^{28} + 224 q^{29} + 96 q^{30} - 188 q^{31} + 502 q^{32} - 219 q^{33} - 261 q^{34} + 624 q^{35} + 972 q^{36} + 223 q^{37} + 737 q^{38} + 183 q^{39} - 562 q^{40} + 106 q^{41} - 729 q^{42} + 607 q^{43} + 767 q^{44} + 225 q^{45} - 529 q^{46} + 1657 q^{47} - 1320 q^{48} + 848 q^{49} + 906 q^{50} - 288 q^{51} + 156 q^{52} + 1902 q^{53} - 162 q^{54} + 1215 q^{55} + 3540 q^{56} - 213 q^{57} + 2871 q^{58} + 2790 q^{59} - 831 q^{60} - 1952 q^{61} + 3134 q^{62} + 450 q^{63} + 1659 q^{64} + 3653 q^{65} - 618 q^{66} + 2932 q^{67} + 7363 q^{68} - 2034 q^{69} + 4509 q^{70} + 4157 q^{71} + 513 q^{72} + 94 q^{73} + 6271 q^{74} - 1791 q^{75} + 2757 q^{76} + 3564 q^{77} - 1005 q^{78} + 2365 q^{79} + 6249 q^{80} + 2106 q^{81} + 2481 q^{82} + 4852 q^{83} - 1062 q^{84} + 640 q^{85} + 5710 q^{86} - 672 q^{87} + 5291 q^{88} + 2504 q^{89} - 288 q^{90} - 812 q^{91} + 9719 q^{92} + 564 q^{93} - 252 q^{94} + 4999 q^{95} - 1506 q^{96} - 302 q^{97} + 14279 q^{98} + 657 q^{99}+O(q^{100}) \) 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 −5.34036 −3.00000 20.5195 7.43719 16.0211 3.04574 −66.8586 9.00000 −39.7173
1.2 −4.87177 −3.00000 15.7341 20.5455 14.6153 −6.52994 −37.6788 9.00000 −100.093
1.3 −4.69882 −3.00000 14.0790 −9.99706 14.0965 −11.7218 −28.5639 9.00000 46.9744
1.4 −4.43401 −3.00000 11.6604 9.05783 13.3020 −1.54978 −16.2303 9.00000 −40.1625
1.5 −4.21681 −3.00000 9.78151 −11.4954 12.6504 −2.39021 −7.51230 9.00000 48.4738
1.6 −3.30810 −3.00000 2.94355 −9.53218 9.92431 −3.95546 16.7273 9.00000 31.5334
1.7 −2.52525 −3.00000 −1.62309 −7.55105 7.57576 27.7773 24.3007 9.00000 19.0683
1.8 −2.50928 −3.00000 −1.70353 −6.49815 7.52783 −11.5668 24.3488 9.00000 16.3057
1.9 −1.70446 −3.00000 −5.09481 6.00987 5.11339 4.36523 22.3196 9.00000 −10.2436
1.10 −1.46631 −3.00000 −5.84993 20.5962 4.39893 10.7901 20.3083 9.00000 −30.2004
1.11 −1.29051 −3.00000 −6.33458 12.2182 3.87153 −28.0574 18.4989 9.00000 −15.7677
1.12 −0.856736 −3.00000 −7.26600 −16.4216 2.57021 24.6953 13.0789 9.00000 14.0690
1.13 0.289756 −3.00000 −7.91604 2.61839 −0.869268 26.2157 −4.61177 9.00000 0.758695
1.14 0.470819 −3.00000 −7.77833 −2.59445 −1.41246 −14.7664 −7.42874 9.00000 −1.22152
1.15 1.01862 −3.00000 −6.96242 11.3752 −3.05585 27.4472 −15.2410 9.00000 11.5869
1.16 1.84592 −3.00000 −4.59258 −4.86039 −5.53776 −32.4557 −23.2449 9.00000 −8.97190
1.17 2.49832 −3.00000 −1.75838 −8.94013 −7.49497 5.02130 −24.3796 9.00000 −22.3353
1.18 2.51868 −3.00000 −1.65626 17.6341 −7.55603 −25.6392 −24.3210 9.00000 44.4145
1.19 2.98096 −3.00000 0.886122 −19.9669 −8.94288 −13.4057 −21.2062 9.00000 −59.5204
1.20 3.12278 −3.00000 1.75178 1.07358 −9.36835 20.7048 −19.5118 9.00000 3.35257
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(211\) \(1\)

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 633.4.a.d ✓ 26
3.b odd 2 1 1899.4.a.d 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
633.4.a.d ✓ 26 1.a even 1 1 trivial
1899.4.a.d 26 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{26} - 6 T_{2}^{25} - 140 T_{2}^{24} + 861 T_{2}^{23} + 8408 T_{2}^{22} - 53438 T_{2}^{21} + \cdots + 21685862400 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(633))\). Copy content Toggle raw display