## Defining parameters

 Level: $$N$$ = $$77 = 7 \cdot 11$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$480$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(77))$$.

Total New Old
Modular forms 64 48 16
Cusp forms 4 4 0
Eisenstein series 60 44 16

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4q - 2q^{2} - 3q^{4} - q^{7} + q^{8} - q^{9} + O(q^{10})$$ $$4q - 2q^{2} - 3q^{4} - q^{7} + q^{8} - q^{9} - q^{11} + 3q^{14} + 3q^{18} - 2q^{22} - 2q^{23} - q^{25} + 2q^{28} - 2q^{29} + 4q^{32} - 3q^{36} + 3q^{37} - 2q^{43} + 2q^{44} + q^{46} - q^{49} - 2q^{50} + 3q^{53} - 4q^{56} + q^{58} - q^{63} - 2q^{64} - 2q^{67} + 3q^{71} + q^{72} - 4q^{74} - q^{77} + 3q^{79} - q^{81} + q^{86} + q^{88} + 4q^{92} - 2q^{98} + 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(77))$$

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
77.1.c $$\chi_{77}(43, \cdot)$$ None 0 1
77.1.d $$\chi_{77}(34, \cdot)$$ None 0 1
77.1.g $$\chi_{77}(12, \cdot)$$ None 0 2
77.1.h $$\chi_{77}(32, \cdot)$$ None 0 2
77.1.j $$\chi_{77}(20, \cdot)$$ 77.1.j.a 4 4
77.1.k $$\chi_{77}(8, \cdot)$$ None 0 4
77.1.o $$\chi_{77}(2, \cdot)$$ None 0 8
77.1.p $$\chi_{77}(3, \cdot)$$ None 0 8