# Properties

 Label 1875.2.b Level $1875$ Weight $2$ Character orbit 1875.b Rep. character $\chi_{1875}(1249,\cdot)$ Character field $\Q$ Dimension $80$ Newform subspaces $8$ Sturm bound $500$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1875 = 3 \cdot 5^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1875.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$500$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1875, [\chi])$$.

Total New Old
Modular forms 280 80 200
Cusp forms 220 80 140
Eisenstein series 60 0 60

## Trace form

 $$80 q - 80 q^{4} - 80 q^{9} + O(q^{10})$$ $$80 q - 80 q^{4} - 80 q^{9} + 80 q^{16} - 10 q^{19} + 10 q^{21} - 20 q^{26} + 20 q^{29} + 10 q^{31} + 20 q^{34} + 80 q^{36} - 10 q^{39} - 20 q^{41} - 60 q^{44} + 60 q^{46} - 90 q^{49} + 60 q^{56} - 10 q^{61} - 140 q^{64} - 40 q^{74} + 40 q^{76} - 40 q^{79} + 80 q^{81} - 40 q^{84} + 60 q^{86} + 20 q^{89} + 50 q^{91} + 40 q^{94} - 40 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1875, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1875.2.b.a $4$ $14.972$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots$$
1875.2.b.b $4$ $14.972$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{3}q^{3}+q^{4}+q^{6}+(-4\beta _{1}+\cdots)q^{7}+\cdots$$
1875.2.b.c $8$ $14.972$ 8.0.$$\cdots$$.12 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-2+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$$
1875.2.b.d $8$ $14.972$ 8.0.324000000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}-\beta _{7})q^{2}+\beta _{5}q^{3}-\beta _{4}q^{4}+\cdots$$
1875.2.b.e $12$ $14.972$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{11}q^{6}+\cdots$$
1875.2.b.f $12$ $14.972$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$$
1875.2.b.g $16$ $14.972$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{2})q^{2}+\beta _{11}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$$
1875.2.b.h $16$ $14.972$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}-\beta _{9})q^{2}-\beta _{9}q^{3}+(-1-\beta _{14}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1875, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1875, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(125, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(375, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(625, [\chi])$$$$^{\oplus 2}$$