# Properties

 Label 528.8 Level 528 Weight 8 Dimension 22220 Nonzero newspaces 16 Sturm bound 122880 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$528 = 2^{4} \cdot 3 \cdot 11$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$16$$ Sturm bound: $$122880$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(528))$$.

Total New Old
Modular forms 54320 22384 31936
Cusp forms 53200 22220 30980
Eisenstein series 1120 164 956

## Trace form

 $$22220 q + 43 q^{3} - 760 q^{4} + 556 q^{5} - 364 q^{6} + 626 q^{7} - 4008 q^{8} - 3503 q^{9} + O(q^{10})$$ $$22220 q + 43 q^{3} - 760 q^{4} + 556 q^{5} - 364 q^{6} + 626 q^{7} - 4008 q^{8} - 3503 q^{9} + 51864 q^{10} + 3612 q^{11} - 54744 q^{12} - 6086 q^{13} + 88056 q^{14} - 67515 q^{15} + 105528 q^{16} - 2908 q^{17} - 83188 q^{18} + 366050 q^{19} - 164000 q^{20} + 15764 q^{21} + 99744 q^{22} - 461968 q^{23} + 552724 q^{24} + 243592 q^{25} - 727960 q^{26} - 436733 q^{27} - 259880 q^{28} + 17468 q^{29} + 330740 q^{30} + 696898 q^{31} + 1142400 q^{32} - 401409 q^{33} + 2377888 q^{34} - 1793220 q^{35} - 1659444 q^{36} + 2466978 q^{37} - 3843152 q^{38} + 1756553 q^{39} - 1681592 q^{40} - 2610844 q^{41} + 6240148 q^{42} - 3477756 q^{43} - 1417400 q^{44} - 3967418 q^{45} + 3908952 q^{46} + 2934780 q^{47} - 1806164 q^{48} + 4505084 q^{49} - 4139976 q^{50} + 5873097 q^{51} + 9200760 q^{52} + 1552836 q^{53} - 565116 q^{54} - 18088098 q^{55} - 19533696 q^{56} - 4150953 q^{57} - 6628792 q^{58} - 6279512 q^{59} + 10948668 q^{60} + 17309690 q^{61} + 29438088 q^{62} + 4467297 q^{63} - 154024 q^{64} - 927576 q^{65} + 421056 q^{66} - 40628732 q^{67} - 19963072 q^{68} - 12834714 q^{69} - 61226736 q^{70} + 642908 q^{71} + 10015676 q^{72} + 91148690 q^{73} + 81497264 q^{74} + 27384263 q^{75} + 43829688 q^{76} - 20260112 q^{77} - 45369064 q^{78} - 92223010 q^{79} - 179085384 q^{80} + 36039905 q^{81} - 58781512 q^{82} - 5661004 q^{83} + 68922764 q^{84} + 157956486 q^{85} + 124859040 q^{86} + 116859848 q^{87} + 310193688 q^{88} + 47916692 q^{89} - 30543540 q^{90} + 8118602 q^{91} - 37419936 q^{92} - 32065449 q^{93} - 128967000 q^{94} - 211962228 q^{95} - 74268268 q^{96} - 119377390 q^{97} - 258725400 q^{98} + 2945629 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(528))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
528.8.a $$\chi_{528}(1, \cdot)$$ 528.8.a.a 1 1
528.8.a.b 1
528.8.a.c 1
528.8.a.d 2
528.8.a.e 2
528.8.a.f 2
528.8.a.g 2
528.8.a.h 2
528.8.a.i 2
528.8.a.j 2
528.8.a.k 2
528.8.a.l 2
528.8.a.m 3
528.8.a.n 3
528.8.a.o 3
528.8.a.p 3
528.8.a.q 4
528.8.a.r 4
528.8.a.s 4
528.8.a.t 5
528.8.a.u 5
528.8.a.v 5
528.8.a.w 5
528.8.a.x 5
528.8.b $$\chi_{528}(65, \cdot)$$ n/a 166 1
528.8.d $$\chi_{528}(287, \cdot)$$ n/a 140 1
528.8.f $$\chi_{528}(265, \cdot)$$ None 0 1
528.8.h $$\chi_{528}(439, \cdot)$$ None 0 1
528.8.k $$\chi_{528}(23, \cdot)$$ None 0 1
528.8.m $$\chi_{528}(329, \cdot)$$ None 0 1
528.8.o $$\chi_{528}(175, \cdot)$$ 528.8.o.a 28 1
528.8.o.b 56
528.8.q $$\chi_{528}(43, \cdot)$$ n/a 672 2
528.8.t $$\chi_{528}(133, \cdot)$$ n/a 560 2
528.8.u $$\chi_{528}(155, \cdot)$$ n/a 1120 2
528.8.x $$\chi_{528}(197, \cdot)$$ n/a 1336 2
528.8.y $$\chi_{528}(49, \cdot)$$ n/a 336 4
528.8.ba $$\chi_{528}(79, \cdot)$$ n/a 336 4
528.8.bc $$\chi_{528}(41, \cdot)$$ None 0 4
528.8.be $$\chi_{528}(71, \cdot)$$ None 0 4
528.8.bh $$\chi_{528}(7, \cdot)$$ None 0 4
528.8.bj $$\chi_{528}(25, \cdot)$$ None 0 4
528.8.bl $$\chi_{528}(47, \cdot)$$ n/a 672 4
528.8.bn $$\chi_{528}(17, \cdot)$$ n/a 664 4
528.8.bo $$\chi_{528}(29, \cdot)$$ n/a 5344 8
528.8.br $$\chi_{528}(59, \cdot)$$ n/a 5344 8
528.8.bs $$\chi_{528}(37, \cdot)$$ n/a 2688 8
528.8.bv $$\chi_{528}(19, \cdot)$$ n/a 2688 8

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

## Decomposition of $$S_{8}^{\mathrm{old}}(\Gamma_1(528))$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(\Gamma_1(528)) \cong$$ $$S_{8}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 10}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 10}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 5}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 3}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 2}$$