# Properties

 Label 375.2.b Level $375$ Weight $2$ Character orbit 375.b Rep. character $\chi_{375}(124,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $3$ Sturm bound $100$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$375 = 3 \cdot 5^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 375.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$100$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(375, [\chi])$$.

Total New Old
Modular forms 60 16 44
Cusp forms 40 16 24
Eisenstein series 20 0 20

## Trace form

 $$16 q - 18 q^{4} + 2 q^{6} - 16 q^{9} + O(q^{10})$$ $$16 q - 18 q^{4} + 2 q^{6} - 16 q^{9} + 4 q^{11} - 12 q^{14} + 30 q^{16} + 8 q^{19} - 16 q^{21} - 6 q^{24} + 12 q^{26} - 4 q^{29} - 4 q^{31} - 16 q^{34} + 18 q^{36} + 12 q^{39} + 16 q^{41} + 76 q^{44} - 84 q^{46} - 20 q^{49} + 8 q^{51} - 2 q^{54} - 60 q^{56} - 28 q^{59} + 38 q^{64} + 16 q^{66} - 12 q^{69} + 32 q^{71} + 68 q^{74} - 12 q^{76} + 40 q^{79} + 16 q^{81} + 52 q^{84} - 56 q^{86} - 32 q^{89} - 44 q^{91} + 2 q^{94} - 36 q^{96} - 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(375, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
375.2.b.a $4$ $2.994$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+3\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots$$
375.2.b.b $4$ $2.994$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots$$
375.2.b.c $8$ $2.994$ 8.0.1632160000.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{7})q^{2}-\beta _{4}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(375, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(375, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(125, [\chi])$$$$^{\oplus 2}$$