# Properties

 Label 441.3 Level 441 Weight 3 Dimension 10502 Nonzero newspaces 20 Newform subspaces 83 Sturm bound 42336 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$20$$ Newform subspaces: $$83$$ Sturm bound: $$42336$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(441))$$.

Total New Old
Modular forms 14592 10938 3654
Cusp forms 13632 10502 3130
Eisenstein series 960 436 524

## Trace form

 $$10502 q - 48 q^{2} - 63 q^{3} - 62 q^{4} - 45 q^{5} - 51 q^{6} - 50 q^{7} - 87 q^{8} - 69 q^{9} + O(q^{10})$$ $$10502 q - 48 q^{2} - 63 q^{3} - 62 q^{4} - 45 q^{5} - 51 q^{6} - 50 q^{7} - 87 q^{8} - 69 q^{9} - 153 q^{10} - 42 q^{11} - 6 q^{12} + 9 q^{13} + 66 q^{14} + 12 q^{15} + 302 q^{16} + 165 q^{17} + 36 q^{18} - 63 q^{19} - 33 q^{20} - 90 q^{21} - 318 q^{22} - 351 q^{23} - 393 q^{24} - 394 q^{25} - 531 q^{26} - 258 q^{27} - 450 q^{28} - 339 q^{29} + 18 q^{30} + 309 q^{31} + 582 q^{32} + 333 q^{33} + 930 q^{34} + 375 q^{35} + 483 q^{36} + 559 q^{37} + 1056 q^{38} + 60 q^{39} + 1323 q^{40} + 246 q^{41} - 138 q^{42} - 130 q^{43} - 375 q^{44} - 498 q^{45} - 885 q^{46} - 957 q^{47} - 1731 q^{48} - 444 q^{49} - 2871 q^{50} - 1491 q^{51} - 1447 q^{52} - 1941 q^{53} - 2025 q^{54} - 1224 q^{55} - 2034 q^{56} - 621 q^{57} - 813 q^{58} - 606 q^{59} - 702 q^{60} - 652 q^{61} - 651 q^{62} + 12 q^{63} - 983 q^{64} + 825 q^{65} + 1014 q^{66} + 268 q^{67} + 2682 q^{68} + 1788 q^{69} + 711 q^{70} + 2415 q^{71} + 3927 q^{72} + 1221 q^{73} + 3711 q^{74} + 2613 q^{75} + 834 q^{76} + 1035 q^{77} + 2304 q^{78} + 655 q^{79} + 3540 q^{80} + 195 q^{81} + 1860 q^{82} + 1065 q^{83} + 36 q^{84} + 285 q^{85} + 1203 q^{86} - 258 q^{87} + 2487 q^{88} + 405 q^{89} - 258 q^{90} + 67 q^{91} + 942 q^{92} - 384 q^{93} - 648 q^{94} - 1377 q^{95} - 1020 q^{96} - 1371 q^{97} - 1320 q^{98} - 1248 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(441))$$

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
441.3.b $$\chi_{441}(197, \cdot)$$ 441.3.b.a 4 1
441.3.b.b 4
441.3.b.c 6
441.3.b.d 6
441.3.b.e 8
441.3.d $$\chi_{441}(244, \cdot)$$ 441.3.d.a 2 1
441.3.d.b 2
441.3.d.c 2
441.3.d.d 2
441.3.d.e 4
441.3.d.f 4
441.3.d.g 8
441.3.d.h 8
441.3.j $$\chi_{441}(263, \cdot)$$ 441.3.j.a 2 2
441.3.j.b 2
441.3.j.c 6
441.3.j.d 8
441.3.j.e 16
441.3.j.f 22
441.3.j.g 24
441.3.j.h 24
441.3.j.i 48
441.3.k $$\chi_{441}(31, \cdot)$$ 441.3.k.a 28 2
441.3.k.b 28
441.3.k.c 96
441.3.l $$\chi_{441}(97, \cdot)$$ 441.3.l.a 28 2
441.3.l.b 28
441.3.l.c 96
441.3.m $$\chi_{441}(19, \cdot)$$ 441.3.m.a 2 2
441.3.m.b 2
441.3.m.c 2
441.3.m.d 2
441.3.m.e 2
441.3.m.f 2
441.3.m.g 2
441.3.m.h 4
441.3.m.i 4
441.3.m.j 8
441.3.m.k 8
441.3.m.l 8
441.3.m.m 16
441.3.n $$\chi_{441}(128, \cdot)$$ 441.3.n.a 2 2
441.3.n.b 2
441.3.n.c 6
441.3.n.d 8
441.3.n.e 16
441.3.n.f 22
441.3.n.g 24
441.3.n.h 24
441.3.n.i 48
441.3.q $$\chi_{441}(116, \cdot)$$ 441.3.q.a 8 2
441.3.q.b 8
441.3.q.c 8
441.3.q.d 12
441.3.q.e 16
441.3.r $$\chi_{441}(50, \cdot)$$ 441.3.r.a 2 2
441.3.r.b 6
441.3.r.c 6
441.3.r.d 8
441.3.r.e 16
441.3.r.f 22
441.3.r.g 22
441.3.r.h 24
441.3.r.i 48
441.3.t $$\chi_{441}(166, \cdot)$$ 441.3.t.a 28 2
441.3.t.b 28
441.3.t.c 96
441.3.v $$\chi_{441}(55, \cdot)$$ 441.3.v.a 54 6
441.3.v.b 108
441.3.v.c 108
441.3.x $$\chi_{441}(8, \cdot)$$ 441.3.x.a 216 6
441.3.bc $$\chi_{441}(40, \cdot)$$ 441.3.bc.a 1320 12
441.3.be $$\chi_{441}(29, \cdot)$$ 441.3.be.a 1320 12
441.3.bf $$\chi_{441}(44, \cdot)$$ 441.3.bf.a 456 12
441.3.bi $$\chi_{441}(2, \cdot)$$ 441.3.bi.a 1320 12
441.3.bj $$\chi_{441}(10, \cdot)$$ 441.3.bj.a 12 12
441.3.bj.b 96
441.3.bj.c 108
441.3.bj.d 120
441.3.bj.e 216
441.3.bk $$\chi_{441}(13, \cdot)$$ 441.3.bk.a 1320 12
441.3.bl $$\chi_{441}(61, \cdot)$$ 441.3.bl.a 1320 12
441.3.bm $$\chi_{441}(11, \cdot)$$ 441.3.bm.a 1320 12

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(441))$$ into lower level spaces

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