# Properties

 Label 370.2.c Level $370$ Weight $2$ Character orbit 370.c Rep. character $\chi_{370}(369,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $2$ Sturm bound $114$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$370 = 2 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 370.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$185$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$114$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(370, [\chi])$$.

Total New Old
Modular forms 60 20 40
Cusp forms 52 20 32
Eisenstein series 8 0 8

## Trace form

 $$20q + 20q^{4} - 16q^{9} + O(q^{10})$$ $$20q + 20q^{4} - 16q^{9} + 6q^{10} + 20q^{16} - 24q^{21} + 10q^{25} + 4q^{26} + 20q^{30} - 36q^{34} - 16q^{36} + 6q^{40} - 8q^{41} - 20q^{46} - 16q^{49} + 20q^{64} + 4q^{65} - 40q^{71} + 16q^{74} + 50q^{75} + 116q^{81} - 24q^{84} - 56q^{85} + 20q^{86} - 40q^{90} + 4q^{95} - 164q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(370, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
370.2.c.a $$10$$ $$2.954$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$-10$$ $$0$$ $$-3$$ $$0$$ $$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$$
370.2.c.b $$10$$ $$2.954$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$10$$ $$0$$ $$3$$ $$0$$ $$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(370, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(370, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(185, [\chi])$$$$^{\oplus 2}$$