# Properties

 Label 528.2 Level 528 Weight 2 Dimension 3104 Nonzero newspaces 16 Newform subspaces 57 Sturm bound 30720 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$528 = 2^{4} \cdot 3 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$57$$ Sturm bound: $$30720$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(528))$$.

Total New Old
Modular forms 8240 3268 4972
Cusp forms 7121 3104 4017
Eisenstein series 1119 164 955

## Trace form

 $$3104 q - 13 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{6} - 14 q^{7} + 24 q^{8} + 5 q^{9} + O(q^{10})$$ $$3104 q - 13 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{6} - 14 q^{7} + 24 q^{8} + 5 q^{9} - 24 q^{10} + 12 q^{11} - 40 q^{12} - 30 q^{13} - 24 q^{14} + 5 q^{15} - 72 q^{16} - 4 q^{17} - 36 q^{18} + 2 q^{19} - 32 q^{20} - 28 q^{21} - 56 q^{22} - 16 q^{23} - 76 q^{24} - 28 q^{25} - 40 q^{26} - 37 q^{27} - 40 q^{28} + 20 q^{29} - 60 q^{30} - 62 q^{31} - 17 q^{33} - 64 q^{34} + 12 q^{35} - 52 q^{36} + 58 q^{37} + 16 q^{38} + 9 q^{39} + 8 q^{40} + 92 q^{41} + 68 q^{42} + 20 q^{43} + 40 q^{44} + 38 q^{45} + 56 q^{46} + 60 q^{47} + 108 q^{48} + 80 q^{49} + 72 q^{50} - 23 q^{51} + 24 q^{52} + 12 q^{53} + 76 q^{54} - 2 q^{55} + 31 q^{57} - 72 q^{58} - 56 q^{59} - 36 q^{60} - 158 q^{61} + 24 q^{62} - 31 q^{63} - 168 q^{64} + 24 q^{65} - 72 q^{66} - 92 q^{67} - 64 q^{68} - 66 q^{69} - 464 q^{70} - 4 q^{71} - 132 q^{72} - 230 q^{73} - 304 q^{74} - 17 q^{75} - 488 q^{76} - 176 q^{77} - 376 q^{78} - 98 q^{79} - 456 q^{80} - 59 q^{81} - 488 q^{82} - 28 q^{83} - 244 q^{84} - 394 q^{85} - 288 q^{86} + 8 q^{87} - 648 q^{88} - 148 q^{89} - 52 q^{90} - 22 q^{91} - 288 q^{92} - 153 q^{93} - 440 q^{94} + 12 q^{95} - 108 q^{96} - 262 q^{97} - 360 q^{98} + 29 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(528))$$

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
528.2.a $$\chi_{528}(1, \cdot)$$ 528.2.a.a 1 1
528.2.a.b 1
528.2.a.c 1
528.2.a.d 1
528.2.a.e 1
528.2.a.f 1
528.2.a.g 1
528.2.a.h 1
528.2.a.i 1
528.2.a.j 1
528.2.b $$\chi_{528}(65, \cdot)$$ 528.2.b.a 2 1
528.2.b.b 2
528.2.b.c 2
528.2.b.d 4
528.2.b.e 6
528.2.b.f 6
528.2.d $$\chi_{528}(287, \cdot)$$ 528.2.d.a 2 1
528.2.d.b 2
528.2.d.c 2
528.2.d.d 2
528.2.d.e 2
528.2.d.f 2
528.2.d.g 4
528.2.d.h 4
528.2.f $$\chi_{528}(265, \cdot)$$ None 0 1
528.2.h $$\chi_{528}(439, \cdot)$$ None 0 1
528.2.k $$\chi_{528}(23, \cdot)$$ None 0 1
528.2.m $$\chi_{528}(329, \cdot)$$ None 0 1
528.2.o $$\chi_{528}(175, \cdot)$$ 528.2.o.a 4 1
528.2.o.b 8
528.2.q $$\chi_{528}(43, \cdot)$$ 528.2.q.a 96 2
528.2.t $$\chi_{528}(133, \cdot)$$ 528.2.t.a 40 2
528.2.t.b 40
528.2.u $$\chi_{528}(155, \cdot)$$ 528.2.u.a 160 2
528.2.x $$\chi_{528}(197, \cdot)$$ 528.2.x.a 184 2
528.2.y $$\chi_{528}(49, \cdot)$$ 528.2.y.a 4 4
528.2.y.b 4
528.2.y.c 4
528.2.y.d 4
528.2.y.e 4
528.2.y.f 4
528.2.y.g 4
528.2.y.h 4
528.2.y.i 4
528.2.y.j 4
528.2.y.k 8
528.2.ba $$\chi_{528}(79, \cdot)$$ 528.2.ba.a 8 4
528.2.ba.b 8
528.2.ba.c 32
528.2.bc $$\chi_{528}(41, \cdot)$$ None 0 4
528.2.be $$\chi_{528}(71, \cdot)$$ None 0 4
528.2.bh $$\chi_{528}(7, \cdot)$$ None 0 4
528.2.bj $$\chi_{528}(25, \cdot)$$ None 0 4
528.2.bl $$\chi_{528}(47, \cdot)$$ 528.2.bl.a 32 4
528.2.bl.b 64
528.2.bn $$\chi_{528}(17, \cdot)$$ 528.2.bn.a 8 4
528.2.bn.b 8
528.2.bn.c 8
528.2.bn.d 16
528.2.bn.e 24
528.2.bn.f 24
528.2.bo $$\chi_{528}(29, \cdot)$$ 528.2.bo.a 736 8
528.2.br $$\chi_{528}(59, \cdot)$$ 528.2.br.a 736 8
528.2.bs $$\chi_{528}(37, \cdot)$$ 528.2.bs.a 384 8
528.2.bv $$\chi_{528}(19, \cdot)$$ 528.2.bv.a 384 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(528))$$ into lower level spaces

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