# Properties

 Label 528.4 Level 528 Weight 4 Dimension 9476 Nonzero newspaces 16 Sturm bound 61440 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$528 = 2^{4} \cdot 3 \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$16$$ Sturm bound: $$61440$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(528))$$.

Total New Old
Modular forms 23600 9640 13960
Cusp forms 22480 9476 13004
Eisenstein series 1120 164 956

## Trace form

 $$9476 q - 5 q^{3} + 8 q^{4} - 4 q^{5} - 76 q^{6} - 78 q^{7} - 168 q^{8} - 119 q^{9} + O(q^{10})$$ $$9476 q - 5 q^{3} + 8 q^{4} - 4 q^{5} - 76 q^{6} - 78 q^{7} - 168 q^{8} - 119 q^{9} - 296 q^{10} + 60 q^{11} + 168 q^{12} - 22 q^{13} + 696 q^{14} - 315 q^{15} + 568 q^{16} + 52 q^{17} - 52 q^{18} - 94 q^{19} - 160 q^{20} + 500 q^{21} - 704 q^{22} + 496 q^{23} - 236 q^{24} + 432 q^{25} + 40 q^{26} + 307 q^{27} + 1240 q^{28} - 116 q^{29} + 1460 q^{30} + 1410 q^{31} + 1920 q^{32} + 735 q^{33} + 288 q^{34} + 1500 q^{35} + 972 q^{36} - 2318 q^{37} - 2512 q^{38} - 3319 q^{39} - 4792 q^{40} - 3788 q^{41} - 2732 q^{42} - 3420 q^{43} + 200 q^{44} + 262 q^{45} + 1496 q^{46} - 708 q^{47} - 1364 q^{48} + 1716 q^{49} - 1416 q^{50} + 1929 q^{51} - 2696 q^{52} - 588 q^{53} - 3420 q^{54} + 4062 q^{55} - 2688 q^{56} - 1785 q^{57} - 3064 q^{58} + 1256 q^{59} + 828 q^{60} + 1322 q^{61} + 1992 q^{62} + 417 q^{63} + 4184 q^{64} - 696 q^{65} + 2016 q^{66} + 9284 q^{67} + 3136 q^{68} + 8502 q^{69} + 144 q^{70} - 1124 q^{71} + 2492 q^{72} - 10046 q^{73} - 13520 q^{74} - 5737 q^{75} - 9544 q^{76} - 6352 q^{77} + 5720 q^{78} - 10594 q^{79} + 12216 q^{80} - 775 q^{81} + 21304 q^{82} - 5036 q^{83} + 18572 q^{84} + 15526 q^{85} + 30624 q^{86} + 200 q^{87} + 50712 q^{88} + 13732 q^{89} - 180 q^{90} + 17290 q^{91} + 10848 q^{92} + 15159 q^{93} - 216 q^{94} + 24972 q^{95} - 18796 q^{96} + 514 q^{97} - 23640 q^{98} - 1571 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(528))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
528.4.a $$\chi_{528}(1, \cdot)$$ 528.4.a.a 1 1
528.4.a.b 1
528.4.a.c 1
528.4.a.d 1
528.4.a.e 1
528.4.a.f 1
528.4.a.g 1
528.4.a.h 1
528.4.a.i 1
528.4.a.j 1
528.4.a.k 1
528.4.a.l 1
528.4.a.m 2
528.4.a.n 2
528.4.a.o 2
528.4.a.p 2
528.4.a.q 2
528.4.a.r 2
528.4.a.s 3
528.4.a.t 3
528.4.b $$\chi_{528}(65, \cdot)$$ 528.4.b.a 2 1
528.4.b.b 4
528.4.b.c 6
528.4.b.d 6
528.4.b.e 8
528.4.b.f 8
528.4.b.g 18
528.4.b.h 18
528.4.d $$\chi_{528}(287, \cdot)$$ 528.4.d.a 10 1
528.4.d.b 10
528.4.d.c 20
528.4.d.d 20
528.4.f $$\chi_{528}(265, \cdot)$$ None 0 1
528.4.h $$\chi_{528}(439, \cdot)$$ None 0 1
528.4.k $$\chi_{528}(23, \cdot)$$ None 0 1
528.4.m $$\chi_{528}(329, \cdot)$$ None 0 1
528.4.o $$\chi_{528}(175, \cdot)$$ 528.4.o.a 12 1
528.4.o.b 24
528.4.q $$\chi_{528}(43, \cdot)$$ n/a 288 2
528.4.t $$\chi_{528}(133, \cdot)$$ n/a 240 2
528.4.u $$\chi_{528}(155, \cdot)$$ n/a 480 2
528.4.x $$\chi_{528}(197, \cdot)$$ n/a 568 2
528.4.y $$\chi_{528}(49, \cdot)$$ n/a 144 4
528.4.ba $$\chi_{528}(79, \cdot)$$ n/a 144 4
528.4.bc $$\chi_{528}(41, \cdot)$$ None 0 4
528.4.be $$\chi_{528}(71, \cdot)$$ None 0 4
528.4.bh $$\chi_{528}(7, \cdot)$$ None 0 4
528.4.bj $$\chi_{528}(25, \cdot)$$ None 0 4
528.4.bl $$\chi_{528}(47, \cdot)$$ n/a 288 4
528.4.bn $$\chi_{528}(17, \cdot)$$ n/a 280 4
528.4.bo $$\chi_{528}(29, \cdot)$$ n/a 2272 8
528.4.br $$\chi_{528}(59, \cdot)$$ n/a 2272 8
528.4.bs $$\chi_{528}(37, \cdot)$$ n/a 1152 8
528.4.bv $$\chi_{528}(19, \cdot)$$ n/a 1152 8

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(528))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(528)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(132))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(264))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(528))$$$$^{\oplus 1}$$