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Properties

Label 1899.4.a.d
Level $1899$
Weight $4$
Character orbit 1899.a
Self dual yes
Analytic conductor $112.045$
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] = [1899,4,Mod(1,1899)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1899, 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("1899.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1899 = 3^{2} \cdot 211 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1899.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: \(112.044627101\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: no (minimal twist has level 633)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 6 q^{2} + 108 q^{4} - 25 q^{5} + 50 q^{7} - 57 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q - 6 q^{2} + 108 q^{4} - 25 q^{5} + 50 q^{7} - 57 q^{8} - 32 q^{10} - 73 q^{11} - 61 q^{13} - 243 q^{14} + 440 q^{16} - 96 q^{17} + 71 q^{19} - 277 q^{20} + 206 q^{22} - 678 q^{23} + 597 q^{25} - 335 q^{26} + 354 q^{28} - 224 q^{29} - 188 q^{31} - 502 q^{32} - 261 q^{34} - 624 q^{35} + 223 q^{37} - 737 q^{38} - 562 q^{40} - 106 q^{41} + 607 q^{43} - 767 q^{44} - 529 q^{46} - 1657 q^{47} + 848 q^{49} - 906 q^{50} + 156 q^{52} - 1902 q^{53} + 1215 q^{55} - 3540 q^{56} + 2871 q^{58} - 2790 q^{59} - 1952 q^{61} - 3134 q^{62} + 1659 q^{64} - 3653 q^{65} + 2932 q^{67} - 7363 q^{68} + 4509 q^{70} - 4157 q^{71} + 94 q^{73} - 6271 q^{74} + 2757 q^{76} - 3564 q^{77} + 2365 q^{79} - 6249 q^{80} + 2481 q^{82} - 4852 q^{83} + 640 q^{85} - 5710 q^{86} + 5291 q^{88} - 2504 q^{89} - 812 q^{91} - 9719 q^{92} - 252 q^{94} - 4999 q^{95} - 302 q^{97} - 14279 q^{98}+O(q^{100}) \) 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 −5.46839 0 21.9033 −6.03717 0 −6.24743 −76.0286 0 33.0136
1.2 −5.34200 0 20.5370 −7.44847 0 23.4157 −66.9725 0 39.7897
1.3 −4.88015 0 15.8158 15.7546 0 24.1927 −38.1423 0 −76.8846
1.4 −4.57476 0 12.9284 14.0908 0 −27.9327 −22.5463 0 −64.4620
1.5 −4.48179 0 12.0865 −18.5123 0 33.6992 −18.3147 0 82.9685
1.6 −3.72949 0 5.90908 −12.1387 0 4.84808 7.79805 0 45.2711
1.7 −3.12278 0 1.75178 −1.07358 0 20.7048 19.5118 0 3.35257
1.8 −2.98096 0 0.886122 19.9669 0 −13.4057 21.2062 0 −59.5204
1.9 −2.51868 0 −1.65626 −17.6341 0 −25.6392 24.3210 0 44.4145
1.10 −2.49832 0 −1.75838 8.94013 0 5.02130 24.3796 0 −22.3353
1.11 −1.84592 0 −4.59258 4.86039 0 −32.4557 23.2449 0 −8.97190
1.12 −1.01862 0 −6.96242 −11.3752 0 27.4472 15.2410 0 11.5869
1.13 −0.470819 0 −7.77833 2.59445 0 −14.7664 7.42874 0 −1.22152
1.14 −0.289756 0 −7.91604 −2.61839 0 26.2157 4.61177 0 0.758695
1.15 0.856736 0 −7.26600 16.4216 0 24.6953 −13.0789 0 14.0690
1.16 1.29051 0 −6.33458 −12.2182 0 −28.0574 −18.4989 0 −15.7677
1.17 1.46631 0 −5.84993 −20.5962 0 10.7901 −20.3083 0 −30.2004
1.18 1.70446 0 −5.09481 −6.00987 0 4.36523 −22.3196 0 −10.2436
1.19 2.50928 0 −1.70353 6.49815 0 −11.5668 −24.3488 0 16.3057
1.20 2.52525 0 −1.62309 7.55105 0 27.7773 −24.3007 0 19.0683
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 1899.4.a.d 26
3.b odd 2 1 633.4.a.d ✓ 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
633.4.a.d ✓ 26 3.b odd 2 1
1899.4.a.d 26 1.a even 1 1 trivial

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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1899))\). Copy content Toggle raw display