# Properties

 Label 121.3.h Level $121$ Weight $3$ Character orbit 121.h Rep. character $\chi_{121}(2,\cdot)$ Character field $\Q(\zeta_{110})$ Dimension $840$ Newform subspaces $1$ Sturm bound $33$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$121 = 11^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 121.h (of order $$110$$ and degree $$40$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$121$$ Character field: $$\Q(\zeta_{110})$$ Newform subspaces: $$1$$ Sturm bound: $$33$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(121, [\chi])$$.

Total New Old
Modular forms 920 920 0
Cusp forms 840 840 0
Eisenstein series 80 80 0

## Trace form

 $$840 q - 39 q^{2} - 34 q^{3} - 75 q^{4} - 43 q^{5} - 15 q^{6} - 54 q^{7} - 59 q^{8} - 594 q^{9} + O(q^{10})$$ $$840 q - 39 q^{2} - 34 q^{3} - 75 q^{4} - 43 q^{5} - 15 q^{6} - 54 q^{7} - 59 q^{8} - 594 q^{9} - 132 q^{10} + 10 q^{11} - 79 q^{12} - 79 q^{13} + 6 q^{14} + 156 q^{15} + 5 q^{16} - 44 q^{17} + 69 q^{18} - 69 q^{19} - 84 q^{20} + 55 q^{21} - 97 q^{22} - 180 q^{23} + 138 q^{24} + 44 q^{25} - 14 q^{26} + 173 q^{27} + 16 q^{28} - 4 q^{29} + 135 q^{30} - 11 q^{31} - 44 q^{32} - 10 q^{33} - 62 q^{34} - 124 q^{35} + 115 q^{36} - 228 q^{37} + 398 q^{38} + 5 q^{39} + 5 q^{40} + 36 q^{41} + 39 q^{42} - 44 q^{43} - 211 q^{44} + 330 q^{45} - 74 q^{46} - 44 q^{47} + 125 q^{48} - 5 q^{49} - 1143 q^{50} - 300 q^{51} + 132 q^{52} - 774 q^{53} + 649 q^{54} + 384 q^{55} + 483 q^{56} + 780 q^{57} + 723 q^{58} - 100 q^{59} - 97 q^{60} - 54 q^{61} - 849 q^{62} - 101 q^{63} - 287 q^{64} + 187 q^{65} + 141 q^{66} + 5 q^{67} + 216 q^{68} + 112 q^{69} - 628 q^{70} - 611 q^{71} + 854 q^{72} - 630 q^{73} + 226 q^{74} - 14 q^{75} - 1265 q^{76} - 636 q^{77} + 433 q^{78} - 70 q^{79} - 1539 q^{80} - 868 q^{81} - 531 q^{82} - 269 q^{83} - 35 q^{84} - 370 q^{85} - 185 q^{86} + 55 q^{87} - 1287 q^{88} - 1315 q^{89} - 970 q^{90} - 747 q^{91} - 28 q^{92} + 735 q^{93} - 175 q^{94} + 320 q^{95} + 507 q^{96} + 401 q^{97} + 396 q^{98} + 1740 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(121, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
121.3.h.a $840$ $3.297$ None $$-39$$ $$-34$$ $$-43$$ $$-54$$