# Properties

 Label 441.4 Level 441 Weight 4 Dimension 15863 Nonzero newspaces 20 Sturm bound 56448 Trace bound 3

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## Defining parameters

 Level: $$N$$ = $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$20$$ Sturm bound: $$56448$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(441))$$.

Total New Old
Modular forms 21648 16300 5348
Cusp forms 20688 15863 4825
Eisenstein series 960 437 523

## Trace form

 $$15863 q - 48 q^{2} - 63 q^{3} - 58 q^{4} - 84 q^{5} - 51 q^{6} - 78 q^{7} + 39 q^{8} - 15 q^{9} + O(q^{10})$$ $$15863 q - 48 q^{2} - 63 q^{3} - 58 q^{4} - 84 q^{5} - 51 q^{6} - 78 q^{7} + 39 q^{8} - 15 q^{9} - 69 q^{10} - 111 q^{11} - 312 q^{12} - 398 q^{13} - 606 q^{14} - 321 q^{15} - 94 q^{16} + 573 q^{17} + 828 q^{18} + 1087 q^{19} + 3153 q^{20} + 288 q^{21} + 1692 q^{22} + 510 q^{23} + 417 q^{24} - 469 q^{25} - 1731 q^{26} - 1284 q^{27} - 1794 q^{28} - 2550 q^{29} - 2952 q^{30} - 3548 q^{31} - 6402 q^{32} - 1350 q^{33} - 2232 q^{34} - 66 q^{35} + 987 q^{36} + 463 q^{37} + 4842 q^{38} + 3219 q^{39} + 5013 q^{40} + 5565 q^{41} + 2634 q^{42} + 4039 q^{43} + 11991 q^{44} + 2049 q^{45} + 9123 q^{46} + 3468 q^{47} + 4983 q^{48} + 1908 q^{49} + 2079 q^{50} + 1749 q^{51} - 6449 q^{52} - 4893 q^{53} - 4401 q^{54} - 4341 q^{55} - 5604 q^{56} - 4401 q^{57} + 1533 q^{58} - 8283 q^{59} - 17316 q^{60} + 70 q^{61} - 12543 q^{62} - 5280 q^{63} - 2527 q^{64} - 9012 q^{65} - 13566 q^{66} - 3761 q^{67} - 23460 q^{68} - 10713 q^{69} - 8823 q^{70} - 7629 q^{71} + 1083 q^{72} - 7739 q^{73} + 2205 q^{74} + 12441 q^{75} - 1550 q^{76} + 8280 q^{77} + 24894 q^{78} + 10462 q^{79} + 22422 q^{80} + 12309 q^{81} + 13374 q^{82} + 11760 q^{83} + 7596 q^{84} + 16545 q^{85} + 16179 q^{86} + 2739 q^{87} - 6759 q^{88} + 627 q^{89} - 1644 q^{90} + 4323 q^{91} - 2538 q^{92} - 3633 q^{93} + 7734 q^{94} + 8151 q^{95} - 5628 q^{96} - 1562 q^{97} + 19596 q^{98} - 7863 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(441))$$

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
441.4.a $$\chi_{441}(1, \cdot)$$ 441.4.a.a 1 1
441.4.a.b 1
441.4.a.c 1
441.4.a.d 1
441.4.a.e 1
441.4.a.f 1
441.4.a.g 1
441.4.a.h 1
441.4.a.i 1
441.4.a.j 1
441.4.a.k 1
441.4.a.l 1
441.4.a.m 1
441.4.a.n 2
441.4.a.o 2
441.4.a.p 2
441.4.a.q 2
441.4.a.r 2
441.4.a.s 3
441.4.a.t 3
441.4.a.u 4
441.4.a.v 4
441.4.a.w 4
441.4.a.x 8
441.4.c $$\chi_{441}(440, \cdot)$$ 441.4.c.a 16 1
441.4.c.b 24
441.4.e $$\chi_{441}(226, \cdot)$$ 441.4.e.a 2 2
441.4.e.b 2
441.4.e.c 2
441.4.e.d 2
441.4.e.e 2
441.4.e.f 2
441.4.e.g 2
441.4.e.h 2
441.4.e.i 2
441.4.e.j 2
441.4.e.k 2
441.4.e.l 2
441.4.e.m 2
441.4.e.n 2
441.4.e.o 2
441.4.e.p 4
441.4.e.q 4
441.4.e.r 4
441.4.e.s 4
441.4.e.t 4
441.4.e.u 4
441.4.e.v 4
441.4.e.w 6
441.4.e.x 8
441.4.e.y 8
441.4.e.z 16
441.4.f $$\chi_{441}(148, \cdot)$$ n/a 236 2
441.4.g $$\chi_{441}(67, \cdot)$$ n/a 232 2
441.4.h $$\chi_{441}(214, \cdot)$$ n/a 232 2
441.4.i $$\chi_{441}(68, \cdot)$$ n/a 232 2
441.4.o $$\chi_{441}(146, \cdot)$$ n/a 232 2
441.4.p $$\chi_{441}(80, \cdot)$$ 441.4.p.a 8 2
441.4.p.b 8
441.4.p.c 16
441.4.p.d 48
441.4.s $$\chi_{441}(362, \cdot)$$ n/a 232 2
441.4.u $$\chi_{441}(64, \cdot)$$ n/a 414 6
441.4.w $$\chi_{441}(62, \cdot)$$ n/a 336 6
441.4.y $$\chi_{441}(25, \cdot)$$ n/a 1992 12
441.4.z $$\chi_{441}(4, \cdot)$$ n/a 1992 12
441.4.ba $$\chi_{441}(22, \cdot)$$ n/a 1992 12
441.4.bb $$\chi_{441}(37, \cdot)$$ n/a 828 12
441.4.bd $$\chi_{441}(47, \cdot)$$ n/a 1992 12
441.4.bg $$\chi_{441}(17, \cdot)$$ n/a 672 12
441.4.bh $$\chi_{441}(20, \cdot)$$ n/a 1992 12
441.4.bn $$\chi_{441}(5, \cdot)$$ n/a 1992 12

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(441))$$ into lower level spaces

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