# Properties

 Label 1380.2.f Level $1380$ Weight $2$ Character orbit 1380.f Rep. character $\chi_{1380}(829,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $2$ Sturm bound $576$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1380.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1380, [\chi])$$.

Total New Old
Modular forms 300 20 280
Cusp forms 276 20 256
Eisenstein series 24 0 24

## Trace form

 $$20q - 20q^{9} + O(q^{10})$$ $$20q - 20q^{9} + 4q^{15} + 8q^{19} - 8q^{21} - 4q^{25} - 12q^{29} - 20q^{31} - 12q^{35} + 8q^{39} + 36q^{41} + 16q^{49} - 20q^{59} + 24q^{61} - 32q^{65} + 8q^{69} + 28q^{71} - 8q^{75} - 24q^{79} + 20q^{81} - 36q^{85} - 56q^{89} + 32q^{91} - 16q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1380, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1380.2.f.a $$6$$ $$11.019$$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots$$
1380.2.f.b $$14$$ $$11.019$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{3}+\beta _{10}q^{5}+\beta _{13}q^{7}-q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1380, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1380, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(230, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(345, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(690, [\chi])$$$$^{\oplus 2}$$