Query:
/api/smf_dims/?_offset=0
Table smf_dims
Siegel modular forms
{'111111': '(-34*t**16-39*t**17-38*t**18-76*t**19-62*t**20-41*t**21+4*t**22+27*t**23+56*t**24+56*t**25+46*t**26+17*t**27+7*t**28-4*t**29-19*t**30+31*t**4+48*t**5+61*t**6+81*t**7+67*t**8+47*t**9+t**10-21*t**11-51*t**12-51*t**13-42*t**14-12*t**15)/(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': '(-75*t**22+60*t**21-16*t**20+112*t**19+178*t**18+32*t**17+240*t**16-156*t**15-17*t**14-256*t**13-400*t**12-96*t**11-302*t**10+104*t**9+45*t**8+152*t**7+233*t**6+72*t**5+149*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': '(-112*t**18+211*t**16+192*t**15+401*t**14+263*t**13-292*t**12-481*t**11-557*t**10-624*t**9-139*t**8+304*t**7+282*t**6+376*t**5+235*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': '(-54*t**26+58*t**25+56*t**24+50*t**23+100*t**22-16*t**21+25*t**20-69*t**19-89*t**18-62*t**17-123*t**16+3*t**15+60*t**14-55*t**13-49*t**12-47*t**11-93*t**10+19*t**9-18*t**8+72*t**7+96*t**6+65*t**5+130*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': '(-110*t**26+120*t**25+115*t**24+100*t**23+200*t**22-40*t**21+56*t**20-152*t**19-164*t**18-132*t**17-243*t**16+8*t**15+122*t**14-112*t**13-103*t**12-92*t**11-189*t**10+48*t**9-44*t**8+160*t**7+175*t**6+140*t**5+255*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': '(-153*t**22+36*t**21+371*t**20+342*t**19+302*t**18+423*t**17+506*t**16-243*t**15-921*t**14-845*t**13-764*t**12-997*t**11-694*t**10+245*t**9+590*t**8+542*t**7+502*t**6+613*t**5+381*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': '(-40*t**26+65*t**25+54*t**24+47*t**23+89*t**22-30*t**21+24*t**20-89*t**19-75*t**18-71*t**17-100*t**16+6*t**15+44*t**14-59*t**13-50*t**12-41*t**11-85*t**10+36*t**9-21*t**8+95*t**7+79*t**6+77*t**5+104*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': '(-80*t**26+125*t**25+115*t**24+95*t**23+170*t**22-50*t**21+35*t**20-165*t**19-155*t**18-135*t**17-206*t**16+10*t**15+90*t**14-115*t**13-106*t**12-85*t**11-160*t**10+60*t**9-25*t**8+175*t**7+165*t**6+145*t**5+215*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': '(-63*t**18+42*t**17+211*t**16+192*t**15+289*t**14+130*t**13-334*t**12-482*t**11-493*t**10-470*t**9-55*t**8+304*t**7+283*t**6+312*t**5+193*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': '(-28*t**22+62*t**21+33*t**20+108*t**19+130*t**18+22*t**17+100*t**16-169*t**15-106*t**14-257*t**13-296*t**12-83*t**11-156*t**10+117*t**9+83*t**8+159*t**7+175*t**6+71*t**5+94*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': '(-34*t**16-32*t**17-39*t**18-56*t**19-62*t**20-52*t**21-31*t**22-3*t**23+21*t**24+40*t**25+42*t**26+31*t**27+23*t**28+10*t**29-3*t**30+17*t**4+27*t**5+48*t**6+60*t**7+67*t**8+56*t**9+36*t**10+7*t**11-16*t**12-36*t**13-36*t**14-26*t**15)/(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 $M_{k,58}(Gamma_0(2))$ 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': 6, 'note': ['if $j\\\\ge2 then only $k\\\\ge 4$'], 'space': 'total', 'sym_power': 58, 'title': 'Hilbert Poincare series'}