# Properties

 Label 252.6 Level 252 Weight 6 Dimension 3780 Nonzero newspaces 20 Sturm bound 20736 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$20$$ Sturm bound: $$20736$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(252))$$.

Total New Old
Modular forms 8880 3872 5008
Cusp forms 8400 3780 4620
Eisenstein series 480 92 388

## Trace form

 $$3780 q - 3 q^{2} - 24 q^{3} + 33 q^{4} + 111 q^{5} + 42 q^{6} - 293 q^{7} + 249 q^{8} - 84 q^{9} + O(q^{10})$$ $$3780 q - 3 q^{2} - 24 q^{3} + 33 q^{4} + 111 q^{5} + 42 q^{6} - 293 q^{7} + 249 q^{8} - 84 q^{9} - 2028 q^{10} + 993 q^{11} + 960 q^{12} + 1582 q^{13} + 3369 q^{14} - 3534 q^{15} + 3189 q^{16} - 7419 q^{17} - 3996 q^{18} + 8509 q^{19} + 2466 q^{20} + 6675 q^{21} - 6900 q^{22} - 11217 q^{23} - 4482 q^{24} - 12066 q^{25} - 9282 q^{26} - 846 q^{27} + 8433 q^{28} + 57594 q^{29} - 4998 q^{30} - 13631 q^{31} + 34317 q^{32} - 25686 q^{33} - 4248 q^{34} + 7605 q^{35} + 33918 q^{36} - 4147 q^{37} - 35784 q^{38} - 49542 q^{39} + 13482 q^{40} + 60666 q^{41} - 126750 q^{42} + 2150 q^{43} - 89340 q^{44} + 122430 q^{45} - 13902 q^{46} + 99315 q^{47} + 152910 q^{48} + 273645 q^{49} + 213855 q^{50} - 38304 q^{51} + 159978 q^{52} - 70065 q^{53} - 197964 q^{54} - 181134 q^{55} - 195147 q^{56} + 146904 q^{57} - 270216 q^{58} + 46275 q^{59} - 126558 q^{60} + 279661 q^{61} - 119349 q^{63} + 472869 q^{64} + 61458 q^{65} + 140862 q^{66} + 11367 q^{67} + 523128 q^{68} - 340086 q^{69} - 16410 q^{70} - 126456 q^{71} - 154656 q^{72} + 111577 q^{73} - 690084 q^{74} + 309504 q^{75} - 585048 q^{76} + 36450 q^{77} + 265500 q^{78} + 185793 q^{79} + 707958 q^{80} + 98040 q^{81} + 1067952 q^{82} + 189750 q^{83} + 593298 q^{84} + 49590 q^{85} + 279798 q^{86} - 644112 q^{87} - 397290 q^{88} - 1228635 q^{89} - 781674 q^{90} - 650474 q^{91} - 1814274 q^{92} - 417408 q^{93} - 725394 q^{94} + 998895 q^{95} - 840240 q^{96} + 833734 q^{97} + 46815 q^{98} + 1555206 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(252))$$

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
252.6.a $$\chi_{252}(1, \cdot)$$ 252.6.a.a 1 1
252.6.a.b 1
252.6.a.c 1
252.6.a.d 1
252.6.a.e 2
252.6.a.f 2
252.6.a.g 2
252.6.a.h 2
252.6.b $$\chi_{252}(55, \cdot)$$ 252.6.b.a 2 1
252.6.b.b 4
252.6.b.c 4
252.6.b.d 16
252.6.b.e 20
252.6.b.f 20
252.6.b.g 32
252.6.e $$\chi_{252}(71, \cdot)$$ 252.6.e.a 60 1
252.6.f $$\chi_{252}(125, \cdot)$$ 252.6.f.a 12 1
252.6.i $$\chi_{252}(25, \cdot)$$ 252.6.i.a 80 2
252.6.j $$\chi_{252}(85, \cdot)$$ 252.6.j.a 30 2
252.6.j.b 30
252.6.k $$\chi_{252}(37, \cdot)$$ 252.6.k.a 2 2
252.6.k.b 2
252.6.k.c 2
252.6.k.d 4
252.6.k.e 4
252.6.k.f 8
252.6.k.g 12
252.6.l $$\chi_{252}(193, \cdot)$$ 252.6.l.a 80 2
252.6.n $$\chi_{252}(31, \cdot)$$ n/a 472 2
252.6.o $$\chi_{252}(95, \cdot)$$ n/a 472 2
252.6.t $$\chi_{252}(17, \cdot)$$ 252.6.t.a 28 2
252.6.w $$\chi_{252}(5, \cdot)$$ 252.6.w.a 80 2
252.6.x $$\chi_{252}(41, \cdot)$$ 252.6.x.a 80 2
252.6.ba $$\chi_{252}(155, \cdot)$$ n/a 360 2
252.6.bb $$\chi_{252}(11, \cdot)$$ n/a 472 2
252.6.be $$\chi_{252}(107, \cdot)$$ n/a 160 2
252.6.bf $$\chi_{252}(19, \cdot)$$ n/a 196 2
252.6.bi $$\chi_{252}(139, \cdot)$$ n/a 472 2
252.6.bj $$\chi_{252}(103, \cdot)$$ n/a 472 2
252.6.bm $$\chi_{252}(173, \cdot)$$ 252.6.bm.a 80 2

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(252))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(252)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 9}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 1}$$