Query:
/api/smf_dims/?_offset=0
{'111111': '(81*t**4+123*t**5+161*t**6+208*t**7+171*t**8+108*t**9-10*t**10-75*t**11-153*t**12-152*t**13-122*t**14-45*t**15-97*t**16-107*t**17-108*t**18-201*t**19-164*t**20-100*t**21+17*t**22+83*t**23+160*t**24+159*t**25+128*t**26+52*t**27+22*t**28-9*t**29-47*t**30)/(1+t**27-t**23-t**22-t**21+t**18+t**17+t**16-t**15-t**12+t**11+t**10+t**9-t**6-t**5-t**4)', '21111': '(-196*t**22+168*t**21-33*t**20+318*t**19+494*t**18+108*t**17+668*t**16-414*t**15-31*t**14-708*t**13-1078*t**12-288*t**11-843*t**10+258*t**9+80*t**8+402*t**7+599*t**6+192*t**5+387*t**4)/(1+t**19-t**18+t**17-t**16-t**15+t**14-3*t**13+3*t**12-2*t**11+2*t**10+2*t**9-2*t**8+3*t**7-3*t**6+t**5-t**4-t**3+t**2-t)', '2211': '(-308*t**18+592*t**16+552*t**15+1134*t**14+778*t**13-756*t**12-1303*t**11-1534*t**10-1756*t**9-453*t**8+772*t**7+728*t**6+999*t**5+638*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': '(-156*t**26+165*t**25+159*t**24+147*t**23+294*t**22-36*t**21+101*t**20-194*t**19-220*t**18-177*t**17-341*t**16+5*t**15+164*t**14-160*t**13-150*t**12-142*t**11-285*t**10+41*t**9-92*t**8+199*t**7+229*t**6+182*t**5+350*t**4)/(1+t**23-t**22-t**19+t**18-t**17+t**16+t**13-t**12-t**11+t**10+t**7-t**6+t**5-t**4-t)', '3111': '(-315*t**26+336*t**25+322*t**24+294*t**23+588*t**22-84*t**21+211*t**20-408*t**19-419*t**18-366*t**17-677*t**16+12*t**15+331*t**14-324*t**13-306*t**12-282*t**11-573*t**10+96*t**9-195*t**8+420*t**7+434*t**6+378*t**5+693*t**4)/(1+t**23-t**22-t**19+t**18-t**17+t**16+t**13-t**12-t**11+t**10+t**7-t**6+t**5-t**4-t)', '321': '(-455*t**22+78*t**21+1045*t**20+983*t**19+905*t**18+1292*t**17+1599*t**16-507*t**15-2453*t**14-2303*t**13-2146*t**12-2907*t**11-2142*t**10+483*t**9+1464*t**8+1375*t**7+1297*t**6+1670*t**5+1054*t**4)/(1+t**19-t**17-t**14-2*t**13+t**12+2*t**11+2*t**8+t**7-2*t**6-t**5-t**2)', '33': '(-126*t**26+175*t**25+156*t**24+143*t**23+268*t**22-56*t**21+90*t**20-223*t**19-199*t**18-191*t**17-297*t**16+8*t**15+132*t**14-167*t**13-150*t**12-135*t**11-262*t**10+64*t**9-85*t**8+231*t**7+205*t**6+199*t**5+303*t**4)/(1+t**23-t**22-t**19+t**18-t**17+t**16+t**13-t**12-t**11+t**10+t**7-t**6+t**5-t**4-t)', '411': '(-252*t**26+343*t**25+322*t**24+287*t**23+525*t**22-98*t**21+161*t**20-427*t**19-406*t**18-371*t**17-603*t**16+14*t**15+266*t**14-329*t**13-309*t**12-273*t**11-511*t**10+112*t**9-147*t**8+441*t**7+420*t**6+385*t**5+616*t**4)/(1+t**23-t**22-t**19+t**18-t**17+t**16+t**13-t**12-t**11+t**10+t**7-t**6+t**5-t**4-t)', '42': '(-208*t**18+90*t**17+592*t**16+552*t**15+914*t**14+498*t**13-846*t**12-1304*t**11-1413*t**10-1446*t**9-273*t**8+772*t**7+729*t**6+878*t**5+548*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': '(-99*t**22+171*t**21+67*t**20+312*t**19+396*t**18+93*t**17+379*t**16-433*t**15-218*t**14-709*t**13-870*t**12-269*t**11-545*t**10+276*t**9+165*t**8+411*t**7+487*t**6+190*t**5+279*t**4)/(1+t**19-t**18+t**17-t**16-t**15+t**14-3*t**13+3*t**12-2*t**11+2*t**10+2*t**9-2*t**8+3*t**7-3*t**6+t**5-t**4-t**3+t**2-t)', '6': '(51*t**4+83*t**5+132*t**6+168*t**7+171*t**8+131*t**9+60*t**10-14*t**11-83*t**12-120*t**13-114*t**14-75*t**15-98*t**16-97*t**17-110*t**18-162*t**19-164*t**20-125*t**21-53*t**22+20*t**23+90*t**24+126*t**25+122*t**26+82*t**27+55*t**28+21*t**29-14*t**30)/(1+t**27-t**23-t**22-t**21+t**18+t**17+t**16-t**15-t**12+t**11+t**10+t**9-t**6-t**5-t**4)', 'author': 'Fabien Clery', 'description': 'Hilbert-Poincare series for the sum of the canonical $S_6$-submodule $M_k^p$ ($k\\ge 4$) of $M_{k,82}(Gamma_0(2))$ 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': 41, 'note': ['if $j\\\\ge2 then only $k\\\\ge 4$'], 'space': 'total', 'sym_power': 82, 'title': 'Hilbert Poincare series'}