# Properties

 Label 810.3 Level 810 Weight 3 Dimension 8448 Nonzero newspaces 12 Sturm bound 104976 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$810 = 2 \cdot 3^{4} \cdot 5$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$12$$ Sturm bound: $$104976$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(810))$$.

Total New Old
Modular forms 35856 8448 27408
Cusp forms 34128 8448 25680
Eisenstein series 1728 0 1728

## Trace form

 $$8448 q + 18 q^{5} + 12 q^{7} + O(q^{10})$$ $$8448 q + 18 q^{5} + 12 q^{7} - 12 q^{10} - 36 q^{11} - 12 q^{13} - 72 q^{14} - 144 q^{18} - 360 q^{19} - 180 q^{20} - 540 q^{21} - 168 q^{22} - 684 q^{23} - 90 q^{25} + 108 q^{27} + 96 q^{28} + 612 q^{29} + 216 q^{30} + 468 q^{31} + 756 q^{33} + 216 q^{34} + 324 q^{35} + 360 q^{36} + 336 q^{37} + 144 q^{38} - 72 q^{40} - 900 q^{41} - 564 q^{43} - 432 q^{45} + 48 q^{46} - 1044 q^{47} + 60 q^{49} + 576 q^{50} - 252 q^{51} + 216 q^{52} + 1080 q^{53} + 708 q^{55} + 144 q^{56} + 432 q^{57} + 312 q^{58} + 1620 q^{59} + 828 q^{61} + 1080 q^{63} + 96 q^{64} + 1746 q^{65} + 2016 q^{66} - 684 q^{67} + 72 q^{68} + 3744 q^{69} - 564 q^{70} + 1296 q^{71} + 1152 q^{72} - 660 q^{73} + 720 q^{74} - 336 q^{76} - 108 q^{77} + 576 q^{78} - 732 q^{79} - 288 q^{81} + 192 q^{82} - 396 q^{83} - 288 q^{84} + 432 q^{85} - 648 q^{86} - 4032 q^{87} + 336 q^{88} - 2268 q^{89} - 1440 q^{90} - 468 q^{91} - 936 q^{92} - 4248 q^{93} + 1368 q^{94} - 1836 q^{95} - 576 q^{96} + 1572 q^{97} - 1296 q^{98} - 3600 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(810))$$

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
810.3.b $$\chi_{810}(809, \cdot)$$ 810.3.b.a 8 1
810.3.b.b 16
810.3.b.c 24
810.3.d $$\chi_{810}(161, \cdot)$$ 810.3.d.a 8 1
810.3.d.b 8
810.3.d.c 16
810.3.g $$\chi_{810}(163, \cdot)$$ 810.3.g.a 2 2
810.3.g.b 2
810.3.g.c 2
810.3.g.d 2
810.3.g.e 8
810.3.g.f 8
810.3.g.g 12
810.3.g.h 12
810.3.g.i 12
810.3.g.j 12
810.3.g.k 12
810.3.g.l 12
810.3.h $$\chi_{810}(431, \cdot)$$ 810.3.h.a 8 2
810.3.h.b 8
810.3.h.c 16
810.3.h.d 16
810.3.h.e 16
810.3.j $$\chi_{810}(269, \cdot)$$ 810.3.j.a 8 2
810.3.j.b 8
810.3.j.c 8
810.3.j.d 8
810.3.j.e 8
810.3.j.f 8
810.3.j.g 24
810.3.j.h 24
810.3.l $$\chi_{810}(217, \cdot)$$ n/a 192 4
810.3.n $$\chi_{810}(89, \cdot)$$ n/a 216 6
810.3.o $$\chi_{810}(71, \cdot)$$ n/a 144 6
810.3.r $$\chi_{810}(37, \cdot)$$ n/a 432 12
810.3.t $$\chi_{810}(29, \cdot)$$ n/a 1944 18
810.3.u $$\chi_{810}(11, \cdot)$$ n/a 1296 18
810.3.x $$\chi_{810}(7, \cdot)$$ n/a 3888 36

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(810))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(810)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(405))$$$$^{\oplus 2}$$