# Properties

 Label 2151.4 Level 2151 Weight 4 Dimension 405899 Nonzero newspaces 16 Sturm bound 1370880 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$2151 = 3^{2} \cdot 239$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$16$$ Sturm bound: $$1370880$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2151))$$.

Total New Old
Modular forms 515984 408031 107953
Cusp forms 512176 405899 106277
Eisenstein series 3808 2132 1676

## Trace form

 $$405899q - 351q^{2} - 470q^{3} - 331q^{4} - 327q^{5} - 494q^{6} - 383q^{7} - 489q^{8} - 566q^{9} + O(q^{10})$$ $$405899q - 351q^{2} - 470q^{3} - 331q^{4} - 327q^{5} - 494q^{6} - 383q^{7} - 489q^{8} - 566q^{9} - 1095q^{10} - 225q^{11} - 164q^{12} - 239q^{13} - 237q^{14} - 530q^{15} - 499q^{16} - 753q^{17} - 908q^{18} - 875q^{19} - 381q^{20} - 518q^{21} - 423q^{22} - 291q^{23} - 278q^{24} - 349q^{25} + 699q^{26} + 388q^{27} - 1415q^{28} - 459q^{29} - 1052q^{30} - 887q^{31} - 1203q^{32} - 872q^{33} + 237q^{34} - 369q^{35} - 26q^{36} - 1091q^{37} - 1479q^{38} - 1994q^{39} + 171q^{40} - 93q^{41} + 496q^{42} + 859q^{43} + 567q^{44} + 874q^{45} - 15q^{46} + 441q^{47} - 434q^{48} - 1497q^{49} - 1215q^{50} - 1070q^{51} - 3017q^{52} - 573q^{53} - 2906q^{54} - 3579q^{55} - 225q^{56} + 1966q^{57} - 477q^{58} + 1239q^{59} - 404q^{60} + 157q^{61} - 813q^{62} - 1682q^{63} + 2861q^{64} - 27q^{65} + 1504q^{66} + 3379q^{67} + 1029q^{68} - 2258q^{69} + 279q^{70} - 5829q^{71} - 2258q^{72} - 1631q^{73} + 1275q^{74} + 250q^{75} - 2519q^{76} - 687q^{77} + 1504q^{78} - 3731q^{79} - 741q^{80} + 658q^{81} - 8331q^{82} + 1269q^{83} - 1760q^{84} + 831q^{85} - 291q^{86} - 170q^{87} + 2085q^{88} + 1227q^{89} + 1036q^{90} + 4853q^{91} - 2073q^{92} - 50q^{93} + 3843q^{94} - 621q^{95} - 2636q^{96} + 3775q^{97} + 1335q^{98} - 1070q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2151))$$

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
2151.4.a $$\chi_{2151}(1, \cdot)$$ 2151.4.a.a 22 1
2151.4.a.b 28
2151.4.a.c 28
2151.4.a.d 32
2151.4.a.e 32
2151.4.a.f 37
2151.4.a.g 59
2151.4.a.h 59
2151.4.b $$\chi_{2151}(2150, \cdot)$$ n/a 240 1
2151.4.e $$\chi_{2151}(718, \cdot)$$ n/a 1428 2
2151.4.h $$\chi_{2151}(716, \cdot)$$ n/a 1436 2
2151.4.i $$\chi_{2151}(10, \cdot)$$ n/a 1794 6
2151.4.l $$\chi_{2151}(215, \cdot)$$ n/a 1440 6
2151.4.m $$\chi_{2151}(163, \cdot)$$ n/a 4784 16
2151.4.n $$\chi_{2151}(283, \cdot)$$ n/a 8616 12
2151.4.q $$\chi_{2151}(107, \cdot)$$ n/a 3840 16
2151.4.r $$\chi_{2151}(38, \cdot)$$ n/a 8616 12
2151.4.u $$\chi_{2151}(22, \cdot)$$ n/a 22976 32
2151.4.v $$\chi_{2151}(23, \cdot)$$ n/a 22976 32
2151.4.y $$\chi_{2151}(55, \cdot)$$ n/a 28704 96
2151.4.z $$\chi_{2151}(26, \cdot)$$ n/a 23040 96
2151.4.bc $$\chi_{2151}(4, \cdot)$$ n/a 137856 192
2151.4.bf $$\chi_{2151}(14, \cdot)$$ n/a 137856 192

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2151))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2151)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(239))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(717))$$$$^{\oplus 2}$$