# Properties

 Label 380.2.u Level $380$ Weight $2$ Character orbit 380.u Rep. character $\chi_{380}(61,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $36$ Newform subspaces $2$ Sturm bound $120$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.u (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$2$$ Sturm bound: $$120$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(380, [\chi])$$.

Total New Old
Modular forms 396 36 360
Cusp forms 324 36 288
Eisenstein series 72 0 72

## Trace form

 $$36 q + 6 q^{3} + 6 q^{9} + O(q^{10})$$ $$36 q + 6 q^{3} + 6 q^{9} + 18 q^{13} + 24 q^{17} + 6 q^{21} + 12 q^{23} + 18 q^{27} - 42 q^{29} - 12 q^{31} - 12 q^{33} + 6 q^{35} + 24 q^{37} - 96 q^{39} - 12 q^{41} + 6 q^{43} + 6 q^{47} - 18 q^{49} - 18 q^{51} + 60 q^{53} + 42 q^{57} + 48 q^{59} - 24 q^{61} - 18 q^{63} + 18 q^{65} + 24 q^{67} + 18 q^{69} - 36 q^{71} - 42 q^{73} - 12 q^{75} - 36 q^{77} + 6 q^{79} - 6 q^{81} - 36 q^{83} + 12 q^{87} + 12 q^{89} - 48 q^{93} - 36 q^{97} - 18 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(380, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.u.a $18$ $3.034$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{7})q^{3}-\beta _{4}q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots$$
380.2.u.b $18$ $3.034$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+\beta _{13}q^{3}+(\beta _{2}-\beta _{11})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(380, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(380, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$