↑

Properties

Label 880.2.s.b
Level $880$
Weight $2$
Character orbit 880.s
Analytic conductor $7.027$
Analytic rank $0$
Dimension $236$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [880,2,Mod(67,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.67"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.s (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(236\)
Relative dimension: \(118\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 236 q + 8 q^{5} - 4 q^{7} + 12 q^{8} - 240 q^{9} + 16 q^{13} - 12 q^{14} + 4 q^{15} - 8 q^{16} + 8 q^{17} - 12 q^{18} - 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} - 12 q^{25} + 8 q^{26} + 36 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
67.1 −1.41412 + 0.0161187i − 1.83728i 1.99948 − 0.0455877i 0.189659 − 2.22801i 0.0296147 + 2.59814i 1.53097 + 1.53097i −2.82677 + 0.0966957i −0.375600 −0.232288 + 3.15373i
67.2 −1.41332 − 0.0502702i − 0.532873i 1.99495 + 0.142096i 1.23363 + 1.86498i −0.0267876 + 0.753120i 2.22586 + 2.22586i −2.81235 − 0.301113i 2.71605 −1.64975 − 2.69783i
67.3 −1.41043 − 0.103387i 3.26502i 1.97862 + 0.291641i 1.36398 − 1.77188i 0.337562 − 4.60508i −1.90886 − 1.90886i −2.76055 − 0.615904i −7.66036 −2.10698 + 2.35810i
67.4 −1.40641 − 0.148325i − 3.35511i 1.95600 + 0.417212i −2.17290 − 0.527744i −0.497646 + 4.71867i −1.19615 − 1.19615i −2.68906 − 0.876896i −8.25676 2.97772 + 1.06452i
67.5 −1.40594 − 0.152716i 0.973471i 1.95336 + 0.429419i −2.10939 − 0.741927i 0.148664 − 1.36865i 2.82145 + 2.82145i −2.68073 − 0.902047i 2.05235 2.85239 + 1.36525i
67.6 −1.39816 − 0.212464i 1.34278i 1.90972 + 0.594118i 2.17976 + 0.498642i 0.285292 − 1.87743i −1.81122 − 1.81122i −2.54387 − 1.23642i 1.19694 −2.94172 − 1.16030i
67.7 −1.39471 + 0.234031i 2.04754i 1.89046 − 0.652814i 0.304592 + 2.21523i −0.479189 − 2.85574i 0.0893009 + 0.0893009i −2.48387 + 1.35292i −1.19243 −0.943252 − 3.01832i
67.8 −1.38136 + 0.303053i − 2.77952i 1.81632 − 0.837252i 2.01425 + 0.970972i 0.842342 + 3.83952i 2.07831 + 2.07831i −2.25526 + 1.70699i −4.72573 −3.07667 − 0.730838i
67.9 −1.37409 + 0.334495i 0.443369i 1.77623 − 0.919249i 1.62100 − 1.54024i −0.148305 − 0.609227i 1.09979 + 1.09979i −2.13320 + 1.85727i 2.80342 −1.71219 + 2.65865i
67.10 −1.35942 + 0.389851i − 1.88219i 1.69603 − 1.05994i 1.56476 − 1.59735i 0.733775 + 2.55869i −3.59208 − 3.59208i −1.89240 + 2.10210i −0.542651 −1.50444 + 2.78149i
67.11 −1.33707 − 0.460701i 2.47091i 1.57551 + 1.23198i −0.695230 − 2.12524i 1.13835 − 3.30378i 2.24560 + 2.24560i −1.53899 − 2.37308i −3.10539 −0.0495303 + 3.16189i
67.12 −1.32222 − 0.501744i − 1.77142i 1.49651 + 1.32683i 2.10282 + 0.760358i −0.888801 + 2.34220i −2.55271 − 2.55271i −1.31297 − 2.50521i −0.137935 −2.39888 − 2.06044i
67.13 −1.31123 + 0.529799i 0.968673i 1.43863 − 1.38937i −1.36191 − 1.77347i −0.513202 − 1.27015i −3.54228 − 3.54228i −1.15028 + 2.58396i 2.06167 2.72536 + 1.60388i
67.14 −1.29777 − 0.561963i − 1.70103i 1.36839 + 1.45859i −1.15887 + 1.91234i −0.955918 + 2.20754i 2.84936 + 2.84936i −0.956181 − 2.66190i 0.106489 2.57860 − 1.83052i
67.15 −1.29360 + 0.571496i − 1.55898i 1.34678 − 1.47857i −1.93043 + 1.12846i 0.890953 + 2.01670i −0.709294 − 0.709294i −0.897199 + 2.68236i 0.569572 1.85229 − 2.56301i
67.16 −1.26665 − 0.628966i 2.88691i 1.20880 + 1.59336i 1.59326 + 1.56892i 1.81577 − 3.65670i 2.03489 + 2.03489i −0.528960 − 2.77852i −5.33424 −1.03131 − 2.98938i
67.17 −1.26464 + 0.633007i − 2.29999i 1.19861 − 1.60105i −1.68908 − 1.46527i 1.45591 + 2.90865i 2.33412 + 2.33412i −0.502327 + 2.78346i −2.28995 3.06360 + 0.783827i
67.18 −1.26161 − 0.639017i 2.42059i 1.18331 + 1.61238i −1.44299 + 1.70815i 1.54680 − 3.05383i 0.0778459 + 0.0778459i −0.462542 − 2.79035i −2.85924 2.91203 − 1.23292i
67.19 −1.22640 − 0.704239i 1.37887i 1.00809 + 1.72735i −1.41756 + 1.72931i 0.971057 − 1.69105i −3.12035 − 3.12035i −0.0198531 − 2.82836i 1.09871 2.95634 − 1.12252i
67.20 −1.21505 − 0.723637i − 2.67671i 0.952699 + 1.75851i −0.365315 + 2.20602i −1.93697 + 3.25234i −0.502129 − 0.502129i 0.114947 − 2.82609i −4.16477 2.04024 − 2.41608i
See next 80 embeddings (of 236 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 67.118
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
80.j even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 880.2.s.b ✓ 236
5.c odd 4 1 880.2.bk.b yes 236
16.f odd 4 1 880.2.bk.b yes 236
80.j even 4 1 inner 880.2.s.b ✓ 236
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
880.2.s.b ✓ 236 1.a even 1 1 trivial
880.2.s.b ✓ 236 80.j even 4 1 inner
880.2.bk.b yes 236 5.c odd 4 1
880.2.bk.b yes 236 16.f odd 4 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{236} + 474 T_{3}^{234} + 110675 T_{3}^{232} + 16970356 T_{3}^{230} + 1922174037 T_{3}^{228} + \cdots + 19\!\cdots\!84 \) acting on \(S_{2}^{\mathrm{new}}(880, [\chi])\). Copy content Toggle raw display