# Properties

 Label 2268.1 Level 2268 Weight 1 Dimension 64 Nonzero newspaces 7 Newform subspaces 20 Sturm bound 279936 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$2268 = 2^{2} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$7$$ Newform subspaces: $$20$$ Sturm bound: $$279936$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2268))$$.

Total New Old
Modular forms 3473 624 2849
Cusp forms 233 64 169
Eisenstein series 3240 560 2680

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 64 0 0 0

## Trace form

 $$64q - 4q^{4} + q^{7} + O(q^{10})$$ $$64q - 4q^{4} + q^{7} - 2q^{13} + 4q^{19} + 8q^{22} + 10q^{25} - 4q^{28} + 4q^{31} + 2q^{43} - 12q^{46} + 3q^{49} - 4q^{58} + 4q^{61} + 8q^{64} + 4q^{70} + 4q^{73} + 6q^{79} + 14q^{85} - 2q^{91} - 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2268))$$

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
2268.1.c $$\chi_{2268}(1457, \cdot)$$ None 0 1
2268.1.d $$\chi_{2268}(1945, \cdot)$$ None 0 1
2268.1.g $$\chi_{2268}(1135, \cdot)$$ None 0 1
2268.1.h $$\chi_{2268}(2267, \cdot)$$ 2268.1.h.a 8 1
2268.1.m $$\chi_{2268}(53, \cdot)$$ 2268.1.m.a 2 2
2268.1.m.b 2
2268.1.p $$\chi_{2268}(1081, \cdot)$$ 2268.1.p.a 2 2
2268.1.p.b 2
2268.1.q $$\chi_{2268}(647, \cdot)$$ None 0 2
2268.1.r $$\chi_{2268}(215, \cdot)$$ None 0 2
2268.1.s $$\chi_{2268}(755, \cdot)$$ 2268.1.s.a 2 2
2268.1.s.b 2
2268.1.s.c 2
2268.1.s.d 2
2268.1.s.e 8
2268.1.s.f 8
2268.1.s.g 8
2268.1.u $$\chi_{2268}(919, \cdot)$$ None 0 2
2268.1.v $$\chi_{2268}(379, \cdot)$$ None 0 2
2268.1.y $$\chi_{2268}(163, \cdot)$$ None 0 2
2268.1.z $$\chi_{2268}(325, \cdot)$$ None 0 2
2268.1.bc $$\chi_{2268}(433, \cdot)$$ 2268.1.bc.a 2 2
2268.1.bc.b 2
2268.1.bc.c 2
2268.1.bc.d 2
2268.1.bd $$\chi_{2268}(1405, \cdot)$$ 2268.1.bd.a 2 2
2268.1.bd.b 2
2268.1.bg $$\chi_{2268}(701, \cdot)$$ None 0 2
2268.1.bh $$\chi_{2268}(1565, \cdot)$$ 2268.1.bh.a 2 2
2268.1.bh.b 2
2268.1.bk $$\chi_{2268}(485, \cdot)$$ None 0 2
2268.1.bl $$\chi_{2268}(1243, \cdot)$$ None 0 2
2268.1.bn $$\chi_{2268}(1727, \cdot)$$ None 0 2
2268.1.br $$\chi_{2268}(73, \cdot)$$ None 0 6
2268.1.bu $$\chi_{2268}(233, \cdot)$$ None 0 6
2268.1.bv $$\chi_{2268}(251, \cdot)$$ None 0 6
2268.1.bw $$\chi_{2268}(395, \cdot)$$ None 0 6
2268.1.by $$\chi_{2268}(127, \cdot)$$ None 0 6
2268.1.bz $$\chi_{2268}(667, \cdot)$$ None 0 6
2268.1.cb $$\chi_{2268}(197, \cdot)$$ None 0 6
2268.1.ce $$\chi_{2268}(557, \cdot)$$ None 0 6
2268.1.cg $$\chi_{2268}(181, \cdot)$$ None 0 6
2268.1.ch $$\chi_{2268}(397, \cdot)$$ None 0 6
2268.1.cj $$\chi_{2268}(235, \cdot)$$ None 0 6
2268.1.cl $$\chi_{2268}(143, \cdot)$$ None 0 6
2268.1.cp $$\chi_{2268}(137, \cdot)$$ None 0 18
2268.1.cq $$\chi_{2268}(131, \cdot)$$ None 0 18
2268.1.cv $$\chi_{2268}(61, \cdot)$$ None 0 18
2268.1.cw $$\chi_{2268}(13, \cdot)$$ None 0 18
2268.1.cx $$\chi_{2268}(43, \cdot)$$ None 0 18
2268.1.cy $$\chi_{2268}(67, \cdot)$$ None 0 18
2268.1.cz $$\chi_{2268}(83, \cdot)$$ None 0 18
2268.1.da $$\chi_{2268}(47, \cdot)$$ None 0 18
2268.1.db $$\chi_{2268}(65, \cdot)$$ None 0 18
2268.1.dc $$\chi_{2268}(29, \cdot)$$ None 0 18
2268.1.di $$\chi_{2268}(151, \cdot)$$ None 0 18
2268.1.dj $$\chi_{2268}(229, \cdot)$$ None 0 18

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(2268))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(2268)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 9}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(567))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(756))$$$$^{\oplus 2}$$