# Properties

 Label 531.5 Level 531 Weight 5 Dimension 32783 Nonzero newspaces 8 Sturm bound 104400 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$531 = 3^{2} \cdot 59$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$8$$ Sturm bound: $$104400$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(531))$$.

Total New Old
Modular forms 42224 33297 8927
Cusp forms 41296 32783 8513
Eisenstein series 928 514 414

## Trace form

 $$32783q - 81q^{2} - 110q^{3} - 109q^{4} - 63q^{5} + 82q^{6} + q^{7} - 87q^{8} - 314q^{9} + O(q^{10})$$ $$32783q - 81q^{2} - 110q^{3} - 109q^{4} - 63q^{5} + 82q^{6} + q^{7} - 87q^{8} - 314q^{9} - 693q^{10} - 1053q^{11} - 776q^{12} + 373q^{13} + 2205q^{14} + 1936q^{15} + 1019q^{16} - 87q^{17} - 2924q^{18} - 1985q^{19} - 3315q^{20} - 1076q^{21} + 939q^{22} + 477q^{23} + 2782q^{24} + 1487q^{25} - 87q^{26} - 224q^{27} - 3101q^{28} + 2025q^{29} + 2440q^{30} - 1211q^{31} + 2235q^{32} - 674q^{33} - 2625q^{34} - 87q^{35} + 4654q^{36} + 3019q^{37} + 1491q^{38} - 4064q^{39} - 4515q^{40} - 15345q^{41} - 19340q^{42} - 6461q^{43} - 87q^{44} + 8308q^{45} + 60987q^{46} + 27810q^{47} + 13426q^{48} + 1233q^{49} - 39549q^{50} - 5030q^{51} - 47831q^{52} - 23577q^{53} + 694q^{54} - 32670q^{55} - 49275q^{56} - 10850q^{57} - 29758q^{58} + 474q^{59} - 15172q^{60} + 1843q^{61} + 24969q^{62} + 15040q^{63} + 110759q^{64} + 63558q^{65} + 27352q^{66} + 52825q^{67} + 62679q^{68} + 27640q^{69} + 27825q^{70} - 20445q^{71} - 17018q^{72} - 31814q^{73} - 153219q^{74} - 42158q^{75} + 12487q^{76} - 5247q^{77} + 24004q^{78} + 7489q^{79} - 87q^{80} - 36890q^{81} - 11601q^{82} + 3645q^{83} + 12856q^{84} - 14235q^{85} + 75375q^{86} + 43012q^{87} - 25629q^{88} - 87q^{89} - 41696q^{90} - 82477q^{91} - 67359q^{92} - 38624q^{93} + 3153q^{94} + 26637q^{95} + 7228q^{96} + 81127q^{97} + 272658q^{98} + 18136q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(531))$$

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
531.5.b $$\chi_{531}(296, \cdot)$$ 531.5.b.a 76 1
531.5.c $$\chi_{531}(235, \cdot)$$ 531.5.c.a 3 1
531.5.c.b 16
531.5.c.c 40
531.5.c.d 40
531.5.g $$\chi_{531}(58, \cdot)$$ n/a 476 2
531.5.h $$\chi_{531}(119, \cdot)$$ n/a 464 2
531.5.k $$\chi_{531}(10, \cdot)$$ n/a 2772 28
531.5.l $$\chi_{531}(17, \cdot)$$ n/a 2240 28
531.5.n $$\chi_{531}(5, \cdot)$$ n/a 13328 56
531.5.o $$\chi_{531}(13, \cdot)$$ n/a 13328 56

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

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(531))$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(\Gamma_1(531)) \cong$$ $$S_{5}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(177))$$$$^{\oplus 2}$$