# Properties

 Label 667.2 Level 667 Weight 2 Dimension 17797 Nonzero newspaces 12 Newforms 22 Sturm bound 73920 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$667 = 23 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newforms: $$22$$ Sturm bound: $$73920$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(667))$$.

Total New Old
Modular forms 19096 18933 163
Cusp forms 17865 17797 68
Eisenstein series 1231 1136 95

## Trace form

 $$17797q - 267q^{2} - 270q^{3} - 279q^{4} - 276q^{5} - 294q^{6} - 282q^{7} - 303q^{8} - 297q^{9} + O(q^{10})$$ $$17797q - 267q^{2} - 270q^{3} - 279q^{4} - 276q^{5} - 294q^{6} - 282q^{7} - 303q^{8} - 297q^{9} - 312q^{10} - 294q^{11} - 342q^{12} - 300q^{13} - 330q^{14} - 308q^{15} - 307q^{16} - 290q^{17} - 287q^{18} - 296q^{19} - 254q^{20} - 232q^{21} - 244q^{22} - 261q^{23} - 424q^{24} - 251q^{25} - 270q^{26} - 228q^{27} - 198q^{28} - 261q^{29} - 498q^{30} - 276q^{31} - 291q^{32} - 296q^{33} - 306q^{34} - 302q^{35} - 253q^{36} - 256q^{37} - 272q^{38} - 282q^{39} - 310q^{40} - 340q^{41} - 326q^{42} - 302q^{43} - 284q^{44} - 268q^{45} - 167q^{46} - 544q^{47} - 186q^{48} - 185q^{49} - 187q^{50} - 274q^{51} - 108q^{52} - 250q^{53} - 146q^{54} - 118q^{55} - 124q^{56} - 204q^{57} - 11q^{58} - 530q^{59} - 106q^{60} - 244q^{61} - 218q^{62} - 236q^{63} - 211q^{64} - 230q^{65} - 224q^{66} - 306q^{67} - 154q^{68} - 294q^{69} - 520q^{70} - 224q^{71} - 205q^{72} - 310q^{73} - 206q^{74} - 248q^{75} - 168q^{76} - 208q^{77} - 186q^{78} - 266q^{79} - 6q^{80} - 45q^{81} - 304q^{82} - 244q^{83} - 70q^{84} - 150q^{85} - 82q^{86} - 233q^{87} - 478q^{88} - 256q^{89} - 134q^{90} - 228q^{91} - 235q^{92} - 552q^{93} - 336q^{94} - 196q^{95} + 56q^{96} - 200q^{97} - 143q^{98} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(667))$$

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
667.2.a $$\chi_{667}(1, \cdot)$$ 667.2.a.a 10 1
667.2.a.b 12
667.2.a.c 13
667.2.a.d 16
667.2.c $$\chi_{667}(231, \cdot)$$ 667.2.c.a 24 1
667.2.c.b 30
667.2.f $$\chi_{667}(505, \cdot)$$ 667.2.f.a 12 2
667.2.f.b 104
667.2.g $$\chi_{667}(24, \cdot)$$ 667.2.g.a 6 6
667.2.g.b 144
667.2.g.c 186
667.2.h $$\chi_{667}(59, \cdot)$$ 667.2.h.a 280 10
667.2.h.b 280
667.2.j $$\chi_{667}(93, \cdot)$$ 667.2.j.a 144 6
667.2.j.b 180
667.2.m $$\chi_{667}(144, \cdot)$$ 667.2.m.a 580 10
667.2.o $$\chi_{667}(68, \cdot)$$ 667.2.o.a 72 12
667.2.o.b 624
667.2.q $$\chi_{667}(17, \cdot)$$ 667.2.q.a 1160 20
667.2.s $$\chi_{667}(16, \cdot)$$ 667.2.s.a 3480 60
667.2.u $$\chi_{667}(4, \cdot)$$ 667.2.u.a 3480 60
667.2.x $$\chi_{667}(10, \cdot)$$ 667.2.x.a 6960 120

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(667))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(667)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 2}$$