## Defining parameters

 Level: $$N$$ = $$532 = 2^{2} \cdot 7 \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$17280$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(532))$$.

Total New Old
Modular forms 572 184 388
Cusp forms 32 12 20
Eisenstein series 540 172 368

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 8 0 0

## Trace form

 $$12q - 2q^{4} - q^{5} + 4q^{6} + q^{7} - 2q^{9} + O(q^{10})$$ $$12q - 2q^{4} - q^{5} + 4q^{6} + q^{7} - 2q^{9} - q^{11} + 4q^{13} + 2q^{14} + 2q^{16} - 2q^{19} + 2q^{21} - 4q^{22} + 2q^{23} + 2q^{24} - 5q^{25} - 4q^{29} + 2q^{33} + 5q^{35} - 4q^{37} + 2q^{38} - 4q^{41} + 2q^{43} - q^{45} + 4q^{46} - q^{47} - 7q^{49} + 2q^{52} - 2q^{54} - 8q^{55} - 8q^{56} - 4q^{57} + q^{61} + 4q^{62} + q^{63} - 8q^{64} - 4q^{68} - 8q^{69} - 3q^{73} + 3q^{77} - 4q^{78} - 4q^{81} - 4q^{83} + 4q^{84} - 2q^{85} - 2q^{86} + 4q^{88} - 2q^{89} - 2q^{93} - 4q^{94} - q^{95} + 4q^{96} + 4q^{97} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(532))$$

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
532.1.b $$\chi_{532}(531, \cdot)$$ None 0 1
532.1.c $$\chi_{532}(153, \cdot)$$ None 0 1
532.1.d $$\chi_{532}(267, \cdot)$$ None 0 1
532.1.e $$\chi_{532}(113, \cdot)$$ None 0 1
532.1.m $$\chi_{532}(65, \cdot)$$ None 0 2
532.1.n $$\chi_{532}(163, \cdot)$$ 532.1.n.a 4 2
532.1.o $$\chi_{532}(45, \cdot)$$ None 0 2
532.1.p $$\chi_{532}(31, \cdot)$$ None 0 2
532.1.z $$\chi_{532}(353, \cdot)$$ None 0 2
532.1.ba $$\chi_{532}(255, \cdot)$$ None 0 2
532.1.bb $$\chi_{532}(239, \cdot)$$ None 0 2
532.1.bc $$\chi_{532}(37, \cdot)$$ 532.1.bc.a 2 2
532.1.bc.b 2
532.1.bd $$\chi_{532}(39, \cdot)$$ None 0 2
532.1.be $$\chi_{532}(141, \cdot)$$ None 0 2
532.1.bf $$\chi_{532}(27, \cdot)$$ None 0 2
532.1.bg $$\chi_{532}(229, \cdot)$$ None 0 2
532.1.bh $$\chi_{532}(75, \cdot)$$ None 0 2
532.1.bi $$\chi_{532}(125, \cdot)$$ None 0 2
532.1.bj $$\chi_{532}(373, \cdot)$$ None 0 2
532.1.bk $$\chi_{532}(11, \cdot)$$ 532.1.bk.a 4 2
532.1.bt $$\chi_{532}(123, \cdot)$$ None 0 6
532.1.bu $$\chi_{532}(143, \cdot)$$ None 0 6
532.1.bx $$\chi_{532}(17, \cdot)$$ None 0 6
532.1.by $$\chi_{532}(109, \cdot)$$ None 0 6
532.1.bz $$\chi_{532}(29, \cdot)$$ None 0 6
532.1.ca $$\chi_{532}(237, \cdot)$$ None 0 6
532.1.cf $$\chi_{532}(23, \cdot)$$ None 0 6
532.1.cg $$\chi_{532}(3, \cdot)$$ None 0 6
532.1.ch $$\chi_{532}(167, \cdot)$$ None 0 6
532.1.ci $$\chi_{532}(43, \cdot)$$ None 0 6
532.1.ck $$\chi_{532}(5, \cdot)$$ None 0 6
532.1.cl $$\chi_{532}(53, \cdot)$$ None 0 6

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(532))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(532)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 3}$$