# Properties

 Label 368.2.c Level $368$ Weight $2$ Character orbit 368.c Rep. character $\chi_{368}(367,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$368 = 2^{4} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 368.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$92$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(368, [\chi])$$.

Total New Old
Modular forms 54 12 42
Cusp forms 42 12 30
Eisenstein series 12 0 12

## Trace form

 $$12q - 12q^{9} + O(q^{10})$$ $$12q - 12q^{9} - 12q^{25} - 24q^{29} + 24q^{41} + 36q^{49} - 24q^{69} + 72q^{77} - 60q^{81} + 24q^{85} + 24q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(368, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
368.2.c.a $$4$$ $$2.938$$ $$\Q(\sqrt{2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-2q^{9}+3\beta _{1}q^{11}+\cdots$$
368.2.c.b $$8$$ $$2.938$$ 8.0.303595776.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{6}q^{7}+\beta _{7}q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(368, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(368, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(92, [\chi])$$$$^{\oplus 3}$$