Query:
/api/smf_dims/?_offset=0
Table smf_dims
Siegel modular forms
{'111111': '(-16*t**16-20*t**17-18*t**18-40*t**19-33*t**20-23*t**21+t**22+12*t**23+28*t**24+28*t**25+24*t**26+8*t**27+3*t**28-2*t**29-11*t**30+16*t**4+26*t**5+32*t**6+44*t**7+37*t**8+28*t**9+3*t**10-7*t**11-24*t**12-24*t**13-21*t**14-4*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': '(-40*t**22+30*t**21-10*t**20+56*t**19+90*t**18+14*t**17+121*t**16-81*t**15-11*t**14-130*t**13-207*t**12-46*t**11-151*t**10+57*t**9+31*t**8+80*t**7+126*t**6+38*t**5+80*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': '(-57*t**18+106*t**16+94*t**15+199*t**14+126*t**13-156*t**12-248*t**11-282*t**10-312*t**9-60*t**8+166*t**7+151*t**6+198*t**5+122*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': '(-26*t**26+28*t**25+28*t**24+24*t**23+48*t**22-9*t**21+7*t**20-33*t**19-50*t**18-30*t**17-62*t**16+2*t**15+31*t**14-26*t**13-22*t**12-22*t**11-42*t**10+11*t**9-t**8+35*t**7+56*t**6+32*t**5+68*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': '(-54*t**26+60*t**25+58*t**24+48*t**23+96*t**22-24*t**21+19*t**20-78*t**19-89*t**18-66*t**17-122*t**16+6*t**15+64*t**14-54*t**13-48*t**12-42*t**11-87*t**10+30*t**9-9*t**8+84*t**7+98*t**6+72*t**5+132*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': '(-73*t**22+21*t**21+185*t**20+168*t**19+143*t**18+196*t**17+227*t**16-147*t**15-481*t**14-433*t**13-382*t**12-481*t**11-316*t**10+156*t**9+328*t**8+296*t**7+271*t**6+316*t**5+194*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': '(-18*t**26+34*t**25+26*t**24+22*t**23+42*t**22-20*t**21+9*t**20-49*t**19-39*t**18-37*t**17-47*t**16+5*t**15+21*t**14-29*t**13-23*t**12-17*t**11-39*t**10+25*t**9-7*t**8+54*t**7+42*t**6+42*t**5+50*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': '(-36*t**26+64*t**25+58*t**24+44*t**23+78*t**22-32*t**21+8*t**20-88*t**19-82*t**18-68*t**17-99*t**16+8*t**15+44*t**14-56*t**13-51*t**12-36*t**11-70*t**10+40*t**9+96*t**7+90*t**6+76*t**5+106*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': '(-27*t**18+25*t**17+106*t**16+94*t**15+128*t**14+46*t**13-181*t**12-249*t**11-240*t**10-216*t**9-10*t**8+166*t**7+152*t**6+156*t**5+97*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': '(-11*t**22+31*t**21+21*t**20+52*t**19+61*t**18+6*t**17+35*t**16-90*t**15-66*t**14-129*t**13-143*t**12-35*t**11-61*t**10+67*t**9+53*t**8+85*t**7+89*t**6+37*t**5+45*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': '(-16*t**16-14*t**17-19*t**18-27*t**19-33*t**20-29*t**21-21*t**22-6*t**23+6*t**24+18*t**25+21*t**26+16*t**27+13*t**28+6*t**29-t**30+8*t**4+12*t**5+25*t**6+30*t**7+37*t**8+32*t**9+25*t**10+9*t**11-2*t**12-15*t**13-16*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)', 'author': 'Fabien Clery', 'description': 'Hilbert-Poincare series for the sum of the canonical $S_6$-submodule $M_k^p$ ($k\\ge 4$) of $M_{k,46}(Gamma_0(2))$ 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': 28, 'note': ['if $j\\\\ge2 then only $k\\\\ge 4$'], 'space': 'total', 'sym_power': 46, 'title': 'Hilbert Poincare series'}