## Defining parameters

 Level: $$N$$ = $$7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(7))$$.

Total New Old
Modular forms 7 7 0
Cusp forms 1 1 0
Eisenstein series 6 6 0

## Trace form

 $$q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} + O(q^{10})$$ $$q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} - 6q^{11} + 21q^{14} - 11q^{16} - 27q^{18} + 18q^{22} + 18q^{23} + 25q^{25} - 35q^{28} - 54q^{29} + 45q^{32} + 45q^{36} - 38q^{37} + 58q^{43} - 30q^{44} - 54q^{46} + 49q^{49} - 75q^{50} - 6q^{53} + 21q^{56} + 162q^{58} - 63q^{63} - 91q^{64} - 118q^{67} + 114q^{71} - 27q^{72} + 114q^{74} + 42q^{77} - 94q^{79} + 81q^{81} - 174q^{86} + 18q^{88} + 90q^{92} - 147q^{98} - 54q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$

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
7.3.b $$\chi_{7}(6, \cdot)$$ 7.3.b.a 1 1
7.3.d $$\chi_{7}(3, \cdot)$$ None 0 2