Query:
/api/smf_dims/?_offset=0
Table smf_dims
Siegel modular forms
{'111111': '(-43*t**28+31*t**27+31*t**26-16*t**25+102*t**24+61*t**23-10*t**22+29*t**21-t**20-116*t**19-36*t**18-37*t**17-29*t**16-31*t**15-32*t**14+24*t**13-103*t**12-61*t**11+17*t**10-29*t**9+124*t**7+35*t**6+37*t**5+80*t**4)/(1+t**25-t**24+t**22-2*t**21+t**19-t**18+2*t**16-t**15-t**10+2*t**9-t**7+t**6-2*t**4+t**3-t)', '21111': '(-184*t**20+340*t**19-186*t**18+137*t**17+516*t**16-560*t**15+670*t**14-494*t**13-213*t**12+59*t**11-863*t**10+546*t**9-471*t**8+165*t**7+388*t**6-185*t**5+362*t**4)/(1+t**17-2*t**16+2*t**15-t**14-2*t**13+4*t**12-5*t**11+4*t**10-t**9-t**8+4*t**7-5*t**6+4*t**5-2*t**4-t**3+2*t**2-2*t)', '2211': '(-284*t**18+550*t**16+512*t**15+1048*t**14+718*t**13-706*t**12-1214*t**11-1424*t**10-1625*t**9-418*t**8+722*t**7+680*t**6+928*t**5+594*t**4)/(1+t**15-t**13-2*t**11-t**10+2*t**9+t**8+t**7+2*t**6-t**5-2*t**4-t**2)', '222': '(-147*t**24+293*t**23+5*t**22-160*t**21+428*t**20-297*t**19-33*t**18+148*t**17-320*t**16+10*t**15-16*t**14+10*t**13+162*t**12-313*t**11+9*t**10+171*t**9-445*t**8+308*t**7+47*t**6-168*t**5+335*t**4)/(1+t**21-2*t**20+t**19+t**18-3*t**17+3*t**16-t**15-t**14+2*t**13-t**12-t**9+2*t**8-t**7-t**6+3*t**5-3*t**4+t**3+t**2-2*t)', '3111': '(-294*t**24+609*t**23-21*t**22-308*t**21+868*t**20-638*t**19-32*t**18+282*t**17-634*t**16+7*t**15-2*t**14+7*t**13+304*t**12-614*t**11+31*t**10+314*t**9-868*t**8+644*t**7+42*t**6-287*t**5+644*t**4)/(1+t**21-2*t**20+t**19+t**18-3*t**17+3*t**16-t**15-t**14+2*t**13-t**12-t**9+2*t**8-t**7-t**6+3*t**5-3*t**4+t**3+t**2-2*t)', '321': '(-421*t**20+499*t**19+897*t**18-489*t**17+429*t**16+1259*t**15-222*t**14-1531*t**13-533*t**12-74*t**11-1391*t**10-1231*t**9+656*t**8+1044*t**7-334*t**6+575*t**5+975*t**4)/(1+t**17-t**16-t**15+2*t**14-t**13-2*t**12+t**11+2*t**10-t**9-t**8+2*t**7+t**6-2*t**5-t**4+2*t**3-t**2-t)', '33': '(-114*t**24+270*t**23-9*t**22-126*t**21+378*t**20-301*t**19+8*t**18+82*t**17-273*t**16+15*t**15-22*t**14+15*t**13+126*t**12-289*t**11+22*t**10+140*t**9-399*t**8+315*t**7+5*t**6-101*t**5+285*t**4)/(1+t**21-2*t**20+t**19+t**18-3*t**17+3*t**16-t**15-t**14+2*t**13-t**12-t**9+2*t**8-t**7-t**6+3*t**5-3*t**4+t**3+t**2-2*t)', '411': '(-231*t**24+553*t**23-28*t**22-252*t**21+756*t**20-595*t**19-15*t**18+204*t**17-561*t**16+6*t**15+2*t**14+6*t**13+237*t**12-552*t**11+34*t**10+259*t**9-756*t**8+602*t**7+21*t**6-203*t**5+567*t**4)/(1+t**21-2*t**20+t**19+t**18-3*t**17+3*t**16-t**15-t**14+2*t**13-t**12-t**9+2*t**8-t**7-t**6+3*t**5-3*t**4+t**3+t**2-2*t)', '42': '(-194*t**18+81*t**17+550*t**16+512*t**15+849*t**14+466*t**13-787*t**12-1214*t**11-1314*t**10-1346*t**9-256*t**8+722*t**7+680*t**6+818*t**5+514*t**4)/(1+t**15-t**13-2*t**11-t**10+2*t**9+t**8+t**7+2*t**6-t**5-2*t**4-t**2)', '51': '(-90*t**20+249*t**19-92*t**18+127*t**17+338*t**16-389*t**15+399*t**14-413*t**13-204*t**12-29*t**11-585*t**10+379*t**9-297*t**8+176*t**7+285*t**6-86*t**5+259*t**4)/(1+t**17-2*t**16+2*t**15-t**14-2*t**13+4*t**12-5*t**11+4*t**10-t**9-t**8+4*t**7-5*t**6+4*t**5-2*t**4-t**3+2*t**2-2*t)', '6': '(-13*t**28+28*t**27+34*t**26+11*t**25+66*t**24+40*t**23-16*t**22-t**21-28*t**20-80*t**19-45*t**18-28*t**17-32*t**16-29*t**15-34*t**14-4*t**13-66*t**12-41*t**11+25*t**10+28*t**8+87*t**7+45*t**6+27*t**5+53*t**4)/(1+t**25-t**24+t**22-2*t**21+t**19-t**18+2*t**16-t**15-t**10+2*t**9-t**7+t**6-2*t**4+t**3-t)', 'author': 'Fabien Clery', 'description': 'Hilbert-Poincare series for the sum of the canonical $S_6$-submodule $M_k^p$ ($k\\ge 4$) of $M_{k,80}(Gamma_0(2))$ corresponding to the irreducible $S_6$ representation defined by the partition $p$. The action of $S_6$ is given by identifying $S_6$ with the quotient $SP(4,Z)/Gamma(2)$ and letting act $SP(4,Z)$ in the natural way.', 'group': 'Gamma(2)', 'id': 40, 'note': ['if $j\\\\ge2 then only $k\\\\ge 4$'], 'space': 'total', 'sym_power': 80, 'title': 'Hilbert Poincare series'}