# Properties

 Label 121.3 Level 121 Weight 3 Dimension 1120 Nonzero newspaces 4 Newform subspaces 11 Sturm bound 3630 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$121 = 11^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$4$$ Newform subspaces: $$11$$ Sturm bound: $$3630$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(121))$$.

Total New Old
Modular forms 1290 1260 30
Cusp forms 1130 1120 10
Eisenstein series 160 140 20

## Trace form

 $$1120 q - 45 q^{2} - 45 q^{3} - 45 q^{4} - 45 q^{5} - 85 q^{6} - 75 q^{7} - 85 q^{8} - 65 q^{9} + O(q^{10})$$ $$1120 q - 45 q^{2} - 45 q^{3} - 45 q^{4} - 45 q^{5} - 85 q^{6} - 75 q^{7} - 85 q^{8} - 65 q^{9} - 55 q^{10} - 45 q^{11} - 5 q^{12} - 15 q^{13} - 35 q^{14} - 65 q^{15} - 125 q^{16} - 55 q^{17} - 115 q^{18} - 105 q^{19} - 135 q^{20} - 55 q^{21} - 20 q^{22} - 135 q^{23} - 65 q^{24} - 25 q^{25} - 35 q^{26} - 15 q^{27} + 65 q^{28} + 25 q^{29} + 105 q^{30} + 135 q^{31} - 55 q^{32} - 175 q^{33} - 365 q^{34} - 215 q^{35} - 235 q^{36} - 185 q^{37} + 65 q^{38} - 155 q^{39} + 65 q^{40} + 105 q^{41} - 35 q^{42} - 55 q^{43} - 35 q^{44} - 25 q^{45} - 115 q^{46} - 95 q^{47} + 185 q^{48} + 65 q^{49} + 35 q^{50} + 335 q^{51} - 275 q^{52} - 155 q^{53} - 55 q^{54} + 10 q^{55} - 305 q^{56} - 145 q^{57} - 135 q^{58} - 315 q^{59} - 375 q^{60} - 75 q^{61} - 455 q^{62} - 235 q^{63} + 115 q^{64} - 55 q^{65} - 145 q^{66} + 285 q^{67} + 465 q^{68} + 315 q^{69} + 25 q^{70} - 85 q^{71} + 135 q^{72} - 655 q^{73} + 485 q^{74} - 385 q^{75} - 55 q^{76} + 145 q^{77} + 295 q^{78} - 195 q^{79} + 145 q^{80} + 115 q^{81} - 105 q^{82} - 505 q^{83} - 235 q^{84} - 575 q^{85} - 405 q^{86} - 55 q^{87} - 110 q^{88} - 155 q^{89} - 15 q^{90} + 105 q^{91} - 415 q^{92} - 25 q^{93} - 295 q^{94} + 145 q^{95} - 735 q^{96} + 85 q^{97} - 55 q^{98} + 90 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(121))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
121.3.b $$\chi_{121}(120, \cdot)$$ 121.3.b.a 2 1
121.3.b.b 4
121.3.b.c 8
121.3.d $$\chi_{121}(40, \cdot)$$ 121.3.d.a 4 4
121.3.d.b 4
121.3.d.c 4
121.3.d.d 4
121.3.d.e 8
121.3.d.f 32
121.3.f $$\chi_{121}(10, \cdot)$$ 121.3.f.a 210 10
121.3.h $$\chi_{121}(2, \cdot)$$ 121.3.h.a 840 40

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(121))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(121)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$