Query:
/api/smf_dims/?_offset=0
Table smf_dims
Siegel modular forms
{'111111': '(67*t**4+99*t**5+132*t**6+168*t**7+139*t**8+88*t**9-7*t**10-59*t**11-122*t**12-119*t**13-97*t**14-32*t**15-79*t**16-83*t**17-88*t**18-162*t**19-133*t**20-81*t**21+13*t**22+66*t**23+128*t**24+126*t**25+103*t**26+39*t**27+18*t**28-9*t**29-38*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': '(-159*t**22+131*t**21-26*t**20+248*t**19+400*t**18+82*t**17+537*t**16-328*t**15-31*t**14-557*t**13-877*t**12-224*t**11-679*t**10+208*t**9+72*t**8+320*t**7+491*t**6+153*t**5+316*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': '(-244*t**18+472*t**16+438*t**15+897*t**14+612*t**13-612*t**12-1047*t**11-1224*t**10-1394*t**9-353*t**8+628*t**7+590*t**6+802*t**5+512*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': '(-126*t**26+129*t**25+129*t**24+114*t**23+237*t**22-30*t**21+78*t**20-153*t**19-182*t**18-139*t**17-277*t**16+4*t**15+134*t**14-124*t**13-121*t**12-109*t**11-229*t**10+35*t**9-70*t**8+157*t**7+191*t**6+143*t**5+286*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': '(-252*t**26+273*t**25+252*t**24+237*t**23+462*t**22-72*t**21+162*t**20-333*t**19-336*t**18-297*t**17-538*t**16+11*t**15+267*t**14-262*t**13-237*t**12-227*t**11-447*t**10+83*t**9-147*t**8+344*t**7+350*t**6+309*t**5+552*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': '(-359*t**22+66*t**21+833*t**20+780*t**19+713*t**18+1014*t**17+1247*t**16-432*t**15-1977*t**14-1847*t**13-1712*t**12-2302*t**11-1678*t**10+416*t**9+1196*t**8+1118*t**7+1051*t**6+1339*t**5+842*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': '(-96*t**26+138*t**25+126*t**24+110*t**23+211*t**22-49*t**21+66*t**20-179*t**19-163*t**18-151*t**17-235*t**16+8*t**15+101*t**14-131*t**13-120*t**12-103*t**11-205*t**10+56*t**9-61*t**8+187*t**7+168*t**6+159*t**5+240*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': '(-195*t**26+279*t**25+252*t**24+231*t**23+404*t**22-84*t**21+117*t**20-351*t**19-323*t**18-303*t**17-470*t**16+13*t**15+208*t**14-266*t**13-240*t**12-217*t**11-392*t**10+97*t**9-104*t**8+364*t**7+336*t**6+315*t**5+483*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': '(-163*t**18+72*t**17+472*t**16+438*t**15+717*t**14+387*t**13-684*t**12-1047*t**11-1124*t**10-1143*t**9-209*t**8+628*t**7+590*t**6+702*t**5+441*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': '(-75*t**22+135*t**21+60*t**20+243*t**19+315*t**18+66*t**17+288*t**16-348*t**15-192*t**14-558*t**13-696*t**12-203*t**11-422*t**10+226*t**9+145*t**8+328*t**7+393*t**6+150*t**5+222*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': '(43*t**4+66*t**5+108*t**6+135*t**7+140*t**8+105*t**9+51*t**10-9*t**11-64*t**12-94*t**13-90*t**14-57*t**15-81*t**16-75*t**17-90*t**18-129*t**19-133*t**20-99*t**21-44*t**22+15*t**23+71*t**24+99*t**25+97*t**26+63*t**27+45*t**28+15*t**29-11*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 $M_{k,76}(Gamma_0(2))$ 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': 35, 'note': ['if $j\\\\ge2 then only $k\\\\ge 4$'], 'space': 'total', 'sym_power': 76, 'title': 'Hilbert Poincare series'}