# Properties

 Label 900.3.bo Level $900$ Weight $3$ Character orbit 900.bo Rep. character $\chi_{900}(29,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $480$ Sturm bound $540$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.bo (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$225$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$540$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(900, [\chi])$$.

Total New Old
Modular forms 2928 480 2448
Cusp forms 2832 480 2352
Eisenstein series 96 0 96

## Trace form

 $$480q - 36q^{5} + 10q^{9} + O(q^{10})$$ $$480q - 36q^{5} + 10q^{9} + 55q^{15} + 60q^{21} + 12q^{25} - 105q^{27} - 30q^{31} - 25q^{33} - 220q^{39} + 351q^{45} + 225q^{47} + 1680q^{49} - 170q^{51} - 42q^{55} - 135q^{59} + 5q^{63} + 225q^{65} - 195q^{67} - 80q^{69} + 12q^{75} + 360q^{77} - 120q^{79} - 390q^{81} - 48q^{85} + 525q^{87} - 324q^{95} - 430q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(900, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{3}^{\mathrm{old}}(900, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(900, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$