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Properties

Label 633.4.a.c
Level $633$
Weight $4$
Character orbit 633.a
Self dual yes
Analytic conductor $37.348$
Analytic rank $1$
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: \(1\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 6 q^{2} - 78 q^{3} + 100 q^{4} - 18 q^{5} + 18 q^{6} - 92 q^{7} - 135 q^{8} + 234 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q - 6 q^{2} - 78 q^{3} + 100 q^{4} - 18 q^{5} + 18 q^{6} - 92 q^{7} - 135 q^{8} + 234 q^{9} - 62 q^{11} - 300 q^{12} + 66 q^{13} + 167 q^{14} + 54 q^{15} + 472 q^{16} - 62 q^{17} - 54 q^{18} + 90 q^{19} - 227 q^{20} + 276 q^{21} - 178 q^{22} - 806 q^{23} + 405 q^{24} + 588 q^{25} - 173 q^{26} - 702 q^{27} - 558 q^{28} - 110 q^{29} - 276 q^{31} - 1546 q^{32} + 186 q^{33} - 377 q^{34} - 586 q^{35} + 900 q^{36} - 246 q^{37} - 555 q^{38} - 198 q^{39} - 322 q^{40} - 284 q^{41} - 501 q^{42} - 776 q^{43} - 577 q^{44} - 162 q^{45} + 71 q^{46} - 922 q^{47} - 1416 q^{48} + 1222 q^{49} - 1558 q^{50} + 186 q^{51} + 548 q^{52} - 1110 q^{53} + 162 q^{54} - 362 q^{55} - 1912 q^{56} - 270 q^{57} - 2365 q^{58} - 1634 q^{59} + 681 q^{60} + 1626 q^{61} - 3738 q^{62} - 828 q^{63} + 1787 q^{64} - 2560 q^{65} + 534 q^{66} - 1848 q^{67} - 7859 q^{68} + 2418 q^{69} - 4431 q^{70} - 4206 q^{71} - 1215 q^{72} + 302 q^{73} - 2233 q^{74} - 1764 q^{75} - 111 q^{76} - 3398 q^{77} + 519 q^{78} - 1938 q^{79} - 6423 q^{80} + 2106 q^{81} - 1983 q^{82} - 4756 q^{83} + 1674 q^{84} - 342 q^{85} - 7546 q^{86} + 330 q^{87} - 6595 q^{88} - 3492 q^{89} - 486 q^{91} - 14767 q^{92} + 828 q^{93} - 6924 q^{94} - 7182 q^{95} + 4638 q^{96} - 1946 q^{97} - 8643 q^{98} - 558 q^{99}+O(q^{100}) \) 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 −5.57408 −3.00000 23.0704 10.9804 16.7223 4.32861 −84.0038 9.00000 −61.2059
1.2 −5.44042 −3.00000 21.5982 −8.87275 16.3213 −35.7066 −73.9797 9.00000 48.2715
1.3 −5.13045 −3.00000 18.3215 −16.7988 15.3914 23.7789 −52.9541 9.00000 86.1852
1.4 −4.67259 −3.00000 13.8331 −1.89464 14.0178 17.8356 −27.2556 9.00000 8.85285
1.5 −4.16087 −3.00000 9.31282 13.8556 12.4826 −32.4893 −5.46247 9.00000 −57.6512
1.6 −3.73083 −3.00000 5.91908 −19.0674 11.1925 −19.4308 7.76357 9.00000 71.1372
1.7 −3.31492 −3.00000 2.98868 14.8674 9.94476 1.60803 16.6121 9.00000 −49.2841
1.8 −2.82390 −3.00000 −0.0256065 1.23909 8.47169 −11.2776 22.6635 9.00000 −3.49907
1.9 −2.79024 −3.00000 −0.214578 15.7260 8.37071 21.9169 22.9206 9.00000 −43.8794
1.10 −2.12002 −3.00000 −3.50550 4.60720 6.36007 −27.5178 24.3919 9.00000 −9.76737
1.11 −1.25196 −3.00000 −6.43260 −14.8339 3.75587 −35.2552 18.0690 9.00000 18.5714
1.12 −0.648610 −3.00000 −7.57930 −12.2917 1.94583 14.1431 10.1049 9.00000 7.97250
1.13 −0.511942 −3.00000 −7.73792 −18.0483 1.53583 −6.87712 8.05690 9.00000 9.23970
1.14 0.380179 −3.00000 −7.85546 14.5824 −1.14054 −2.26725 −6.02791 9.00000 5.54390
1.15 0.493453 −3.00000 −7.75650 0.103061 −1.48036 1.56456 −7.77509 9.00000 0.0508558
1.16 1.03747 −3.00000 −6.92366 6.52666 −3.11240 −20.8386 −15.4828 9.00000 6.77120
1.17 1.12135 −3.00000 −6.74257 −9.43754 −3.36406 −1.90435 −16.5316 9.00000 −10.5828
1.18 2.08142 −3.00000 −3.66770 17.7573 −6.24425 14.6130 −24.2854 9.00000 36.9604
1.19 2.23056 −3.00000 −3.02461 −16.4409 −6.69168 34.4945 −24.5910 9.00000 −36.6725
1.20 3.12018 −3.00000 1.73550 −2.08792 −9.36053 15.6344 −19.5464 9.00000 −6.51467
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.c ✓ 26
3.b odd 2 1 1899.4.a.e 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
633.4.a.c ✓ 26 1.a even 1 1 trivial
1899.4.a.e 26 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{26} + 6 T_{2}^{25} - 136 T_{2}^{24} - 811 T_{2}^{23} + 8052 T_{2}^{22} + 47454 T_{2}^{21} + \cdots - 4709941632 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(633))\). Copy content Toggle raw display