# Properties

 Label 354.3 Level 354 Weight 3 Dimension 1740 Nonzero newspaces 4 Newform subspaces 4 Sturm bound 20880 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$354 = 2 \cdot 3 \cdot 59$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$4$$ Newform subspaces: $$4$$ Sturm bound: $$20880$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(354))$$.

Total New Old
Modular forms 7192 1740 5452
Cusp forms 6728 1740 4988
Eisenstein series 464 0 464

## Trace form

 $$1740q + O(q^{10})$$ $$1740q + 754q^{45} + 1392q^{46} + 1276q^{47} + 2088q^{49} + 1856q^{50} + 1624q^{51} + 696q^{52} + 1160q^{53} + 812q^{54} + 1044q^{55} + 290q^{57} - 232q^{59} - 348q^{60} - 696q^{61} - 464q^{62} - 1450q^{63} - 2436q^{65} - 1624q^{66} - 2088q^{67} - 1160q^{68} - 2552q^{69} - 2784q^{70} - 3016q^{71} - 1740q^{73} - 1856q^{74} - 986q^{75} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(354))$$

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
354.3.b $$\chi_{354}(119, \cdot)$$ 354.3.b.a 40 1
354.3.d $$\chi_{354}(235, \cdot)$$ 354.3.d.a 20 1
354.3.f $$\chi_{354}(13, \cdot)$$ 354.3.f.a 560 28
354.3.h $$\chi_{354}(5, \cdot)$$ 354.3.h.a 1120 28

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(354))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(354)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(118))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(177))$$$$^{\oplus 2}$$