# Properties

 Label 2672.2 Level 2672 Weight 2 Dimension 124745 Nonzero newspaces 8 Sturm bound 892416 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$2672 = 2^{4} \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$892416$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2672))$$.

Total New Old
Modular forms 225428 126229 99199
Cusp forms 220781 124745 96036
Eisenstein series 4647 1484 3163

## Trace form

 $$124745q - 328q^{2} - 245q^{3} - 332q^{4} - 411q^{5} - 340q^{6} - 249q^{7} - 340q^{8} - 83q^{9} + O(q^{10})$$ $$124745q - 328q^{2} - 245q^{3} - 332q^{4} - 411q^{5} - 340q^{6} - 249q^{7} - 340q^{8} - 83q^{9} - 332q^{10} - 253q^{11} - 324q^{12} - 411q^{13} - 324q^{14} - 257q^{15} - 316q^{16} - 739q^{17} - 336q^{18} - 261q^{19} - 340q^{20} - 423q^{21} - 332q^{22} - 249q^{23} - 332q^{24} - 83q^{25} - 340q^{26} - 233q^{27} - 348q^{28} - 427q^{29} - 324q^{30} - 217q^{31} - 348q^{32} - 739q^{33} - 340q^{34} - 241q^{35} - 324q^{36} - 427q^{37} - 308q^{38} - 249q^{39} - 316q^{40} - 83q^{41} - 332q^{42} - 269q^{43} - 324q^{44} - 419q^{45} - 356q^{46} - 281q^{47} - 348q^{48} - 759q^{49} - 320q^{50} - 257q^{51} - 324q^{52} - 395q^{53} - 332q^{54} - 249q^{55} - 316q^{56} - 83q^{57} - 308q^{58} - 237q^{59} - 332q^{60} - 379q^{61} - 364q^{62} - 257q^{63} - 332q^{64} - 755q^{65} - 340q^{66} - 229q^{67} - 332q^{68} - 391q^{69} - 348q^{70} - 249q^{71} - 340q^{72} - 83q^{73} - 332q^{74} - 261q^{75} - 356q^{76} - 423q^{77} - 324q^{78} - 249q^{79} - 348q^{80} - 767q^{81} - 332q^{82} - 245q^{83} - 316q^{84} - 423q^{85} - 332q^{86} - 249q^{87} - 348q^{88} - 83q^{89} - 324q^{90} - 257q^{91} - 284q^{92} - 447q^{93} - 300q^{94} - 225q^{95} - 300q^{96} - 739q^{97} - 320q^{98} - 245q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2672))$$

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
2672.2.a $$\chi_{2672}(1, \cdot)$$ 2672.2.a.a 1 1
2672.2.a.b 2
2672.2.a.c 2
2672.2.a.d 2
2672.2.a.e 2
2672.2.a.f 2
2672.2.a.g 2
2672.2.a.h 3
2672.2.a.i 3
2672.2.a.j 5
2672.2.a.k 7
2672.2.a.l 7
2672.2.a.m 9
2672.2.a.n 12
2672.2.a.o 12
2672.2.a.p 12
2672.2.b $$\chi_{2672}(2671, \cdot)$$ 2672.2.b.a 28 1
2672.2.b.b 56
2672.2.c $$\chi_{2672}(1337, \cdot)$$ None 0 1
2672.2.h $$\chi_{2672}(1335, \cdot)$$ None 0 1
2672.2.j $$\chi_{2672}(669, \cdot)$$ n/a 664 2
2672.2.l $$\chi_{2672}(667, \cdot)$$ n/a 668 2
2672.2.m $$\chi_{2672}(33, \cdot)$$ n/a 6806 82
2672.2.n $$\chi_{2672}(23, \cdot)$$ None 0 82
2672.2.s $$\chi_{2672}(9, \cdot)$$ None 0 82
2672.2.t $$\chi_{2672}(15, \cdot)$$ n/a 6888 82
2672.2.u $$\chi_{2672}(35, \cdot)$$ n/a 54776 164
2672.2.w $$\chi_{2672}(21, \cdot)$$ n/a 54776 164

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2672))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2672)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(334))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(668))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1336))$$$$^{\oplus 2}$$