## Defining parameters

 Level: $$N$$ = $$1944 = 2^{3} \cdot 3^{5}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$7$$ Newform subspaces: $$14$$ Sturm bound: $$209952$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1944))$$.

Total New Old
Modular forms 2560 516 2044
Cusp forms 292 132 160
Eisenstein series 2268 384 1884

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 114 0 18 0

## Trace form

 $$132q + O(q^{10})$$ $$132q - 12q^{10} - 6q^{19} + 6q^{22} + 6q^{34} + 9q^{38} + 6q^{43} - 12q^{46} - 30q^{55} + 9q^{59} + 6q^{64} + 6q^{67} - 45q^{68} + 6q^{73} - 21q^{76} + 12q^{82} - 21q^{88} + 9q^{89} - 27q^{96} + 6q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1944))$$

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
1944.1.b $$\chi_{1944}(1459, \cdot)$$ None 0 1
1944.1.e $$\chi_{1944}(1457, \cdot)$$ 1944.1.e.a 2 1
1944.1.g $$\chi_{1944}(487, \cdot)$$ None 0 1
1944.1.h $$\chi_{1944}(485, \cdot)$$ 1944.1.h.a 3 1
1944.1.h.b 3
1944.1.h.c 4
1944.1.j $$\chi_{1944}(1133, \cdot)$$ 1944.1.j.a 6 2
1944.1.j.b 6
1944.1.j.c 8
1944.1.k $$\chi_{1944}(1135, \cdot)$$ None 0 2
1944.1.m $$\chi_{1944}(161, \cdot)$$ 1944.1.m.a 4 2
1944.1.p $$\chi_{1944}(163, \cdot)$$ None 0 2
1944.1.r $$\chi_{1944}(379, \cdot)$$ 1944.1.r.a 6 6
1944.1.r.b 6
1944.1.r.c 6
1944.1.r.d 6
1944.1.s $$\chi_{1944}(55, \cdot)$$ None 0 6
1944.1.u $$\chi_{1944}(377, \cdot)$$ None 0 6
1944.1.x $$\chi_{1944}(53, \cdot)$$ None 0 6
1944.1.z $$\chi_{1944}(125, \cdot)$$ None 0 18
1944.1.ba $$\chi_{1944}(127, \cdot)$$ None 0 18
1944.1.bc $$\chi_{1944}(17, \cdot)$$ None 0 18
1944.1.bf $$\chi_{1944}(19, \cdot)$$ 1944.1.bf.a 18 18
1944.1.bh $$\chi_{1944}(43, \cdot)$$ 1944.1.bh.a 54 54
1944.1.bi $$\chi_{1944}(7, \cdot)$$ None 0 54
1944.1.bk $$\chi_{1944}(41, \cdot)$$ None 0 54
1944.1.bn $$\chi_{1944}(5, \cdot)$$ None 0 54

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1944))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1944)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(243))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(648))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(972))$$$$^{\oplus 2}$$