# Properties

 Label 1960.2.g Level $1960$ Weight $2$ Character orbit 1960.g Rep. character $\chi_{1960}(1569,\cdot)$ Character field $\Q$ Dimension $62$ Newform subspaces $7$ Sturm bound $672$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1960 = 2^{3} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1960.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$672$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$3$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1960, [\chi])$$.

Total New Old
Modular forms 368 62 306
Cusp forms 304 62 242
Eisenstein series 64 0 64

## Trace form

 $$62q - 2q^{5} - 66q^{9} + O(q^{10})$$ $$62q - 2q^{5} - 66q^{9} - 4q^{11} + 4q^{15} - 8q^{19} + 14q^{25} + 8q^{29} - 8q^{31} + 24q^{39} - 20q^{41} + 18q^{45} - 48q^{51} + 8q^{55} - 20q^{61} + 16q^{65} + 32q^{69} + 48q^{75} + 40q^{79} + 86q^{81} + 16q^{85} + 36q^{89} - 20q^{95} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1960, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1960.2.g.a $$2$$ $$15.651$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2-i)q^{5}+2q^{9}-q^{11}+\cdots$$
1960.2.g.b $$2$$ $$15.651$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-i)q^{5}-q^{9}-4q^{11}+2iq^{13}+\cdots$$
1960.2.g.c $$6$$ $$15.651$$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$$
1960.2.g.d $$8$$ $$15.651$$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{3}-\beta _{6}q^{5}-\beta _{2}q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots$$
1960.2.g.e $$12$$ $$15.651$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$$
1960.2.g.f $$12$$ $$15.651$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{5}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$$
1960.2.g.g $$20$$ $$15.651$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{17}q^{3}-\beta _{16}q^{5}+(-1+\beta _{1})q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1960, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1960, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(490, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(980, [\chi])$$$$^{\oplus 2}$$