# Properties

 Label 120.3.c Level $120$ Weight $3$ Character orbit 120.c Rep. character $\chi_{120}(89,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $1$ Sturm bound $72$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 120.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$72$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(120, [\chi])$$.

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

## Trace form

 $$12q + 8q^{9} + O(q^{10})$$ $$12q + 8q^{9} + 16q^{15} + 4q^{21} + 36q^{25} - 48q^{31} - 128q^{39} - 68q^{45} - 252q^{49} + 48q^{51} - 48q^{55} + 144q^{61} + 268q^{69} + 304q^{75} + 432q^{79} - 188q^{81} + 336q^{85} - 560q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(120, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
120.3.c.a $$12$$ $$3.270$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(120, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(120, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$