# Properties

 Label 441.2 Level 441 Weight 2 Dimension 5142 Nonzero newspaces 20 Newform subspaces 81 Sturm bound 28224 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$81$$ Sturm bound: $$28224$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(441))$$.

Total New Old
Modular forms 7536 5579 1957
Cusp forms 6577 5142 1435
Eisenstein series 959 437 522

## Trace form

 $$5142 q - 45 q^{2} - 60 q^{3} - 37 q^{4} - 39 q^{5} - 60 q^{6} - 50 q^{7} - 63 q^{8} - 60 q^{9} + O(q^{10})$$ $$5142 q - 45 q^{2} - 60 q^{3} - 37 q^{4} - 39 q^{5} - 60 q^{6} - 50 q^{7} - 63 q^{8} - 60 q^{9} - 105 q^{10} - 27 q^{11} - 84 q^{12} - 31 q^{13} - 60 q^{14} - 132 q^{15} - 69 q^{16} - 87 q^{17} - 108 q^{18} - 157 q^{19} - 135 q^{20} - 90 q^{21} - 117 q^{22} - 75 q^{23} - 132 q^{24} - 45 q^{25} - 111 q^{26} - 96 q^{27} - 156 q^{28} - 81 q^{29} - 144 q^{30} - 43 q^{31} - 141 q^{32} - 108 q^{33} - 87 q^{34} - 87 q^{35} - 228 q^{36} - 189 q^{37} - 213 q^{38} - 132 q^{39} - 285 q^{40} - 225 q^{41} - 138 q^{42} - 143 q^{43} - 321 q^{44} - 156 q^{45} - 363 q^{46} - 141 q^{47} - 36 q^{48} - 150 q^{49} - 246 q^{50} - 60 q^{51} - 233 q^{52} - 21 q^{53} - 198 q^{55} - 102 q^{56} - 12 q^{57} - 75 q^{58} + 87 q^{59} + 144 q^{60} - 68 q^{61} + 207 q^{62} + 12 q^{63} - 169 q^{64} + 81 q^{65} + 24 q^{66} - 39 q^{67} + 177 q^{68} - 12 q^{69} - 87 q^{70} - 93 q^{71} + 48 q^{72} - 217 q^{73} - 87 q^{74} - 84 q^{75} - 139 q^{76} - 99 q^{77} - 180 q^{78} - 135 q^{79} - 198 q^{80} - 228 q^{81} - 330 q^{82} - 279 q^{83} - 216 q^{84} - 249 q^{85} - 462 q^{86} - 240 q^{87} - 450 q^{88} - 411 q^{89} - 384 q^{90} - 311 q^{91} - 528 q^{92} - 288 q^{93} - 432 q^{94} - 459 q^{95} - 336 q^{96} - 280 q^{97} - 480 q^{98} - 384 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$

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

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
441.2.a $$\chi_{441}(1, \cdot)$$ 441.2.a.a 1 1
441.2.a.b 1
441.2.a.c 1
441.2.a.d 1
441.2.a.e 1
441.2.a.f 1
441.2.a.g 2
441.2.a.h 2
441.2.a.i 2
441.2.a.j 2
441.2.c $$\chi_{441}(440, \cdot)$$ 441.2.c.a 4 1
441.2.c.b 8
441.2.e $$\chi_{441}(226, \cdot)$$ 441.2.e.a 2 2
441.2.e.b 2
441.2.e.c 2
441.2.e.d 2
441.2.e.e 2
441.2.e.f 4
441.2.e.g 4
441.2.e.h 4
441.2.e.i 4
441.2.e.j 4
441.2.f $$\chi_{441}(148, \cdot)$$ 441.2.f.a 2 2
441.2.f.b 2
441.2.f.c 6
441.2.f.d 6
441.2.f.e 10
441.2.f.f 10
441.2.f.g 12
441.2.f.h 24
441.2.g $$\chi_{441}(67, \cdot)$$ 441.2.g.a 2 2
441.2.g.b 6
441.2.g.c 6
441.2.g.d 6
441.2.g.e 6
441.2.g.f 10
441.2.g.g 12
441.2.g.h 24
441.2.h $$\chi_{441}(214, \cdot)$$ 441.2.h.a 2 2
441.2.h.b 6
441.2.h.c 6
441.2.h.d 6
441.2.h.e 6
441.2.h.f 10
441.2.h.g 12
441.2.h.h 24
441.2.i $$\chi_{441}(68, \cdot)$$ 441.2.i.a 2 2
441.2.i.b 10
441.2.i.c 12
441.2.i.d 48
441.2.o $$\chi_{441}(146, \cdot)$$ 441.2.o.a 2 2
441.2.o.b 2
441.2.o.c 10
441.2.o.d 10
441.2.o.e 48
441.2.p $$\chi_{441}(80, \cdot)$$ 441.2.p.a 4 2
441.2.p.b 8
441.2.p.c 16
441.2.s $$\chi_{441}(362, \cdot)$$ 441.2.s.a 2 2
441.2.s.b 10
441.2.s.c 12
441.2.s.d 48
441.2.u $$\chi_{441}(64, \cdot)$$ 441.2.u.a 6 6
441.2.u.b 12
441.2.u.c 24
441.2.u.d 36
441.2.u.e 60
441.2.w $$\chi_{441}(62, \cdot)$$ 441.2.w.a 120 6
441.2.y $$\chi_{441}(25, \cdot)$$ 441.2.y.a 648 12
441.2.z $$\chi_{441}(4, \cdot)$$ 441.2.z.a 648 12
441.2.ba $$\chi_{441}(22, \cdot)$$ 441.2.ba.a 648 12
441.2.bb $$\chi_{441}(37, \cdot)$$ 441.2.bb.a 12 12
441.2.bb.b 24
441.2.bb.c 48
441.2.bb.d 48
441.2.bb.e 60
441.2.bb.f 72
441.2.bd $$\chi_{441}(47, \cdot)$$ 441.2.bd.a 648 12
441.2.bg $$\chi_{441}(17, \cdot)$$ 441.2.bg.a 216 12
441.2.bh $$\chi_{441}(20, \cdot)$$ 441.2.bh.a 648 12
441.2.bn $$\chi_{441}(5, \cdot)$$ 441.2.bn.a 648 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(441))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(441)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 1}$$