# Properties

 Label 2175.1.b Level $2175$ Weight $1$ Character orbit 2175.b Rep. character $\chi_{2175}(2174,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $4$ Sturm bound $300$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2175 = 3 \cdot 5^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2175.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$435$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$300$$ Trace bound: $$14$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2175, [\chi])$$.

Total New Old
Modular forms 36 20 16
Cusp forms 24 16 8
Eisenstein series 12 4 8

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16 q - 12 q^{4} - 4 q^{6} - 16 q^{9} + O(q^{10})$$ $$16 q - 12 q^{4} - 4 q^{6} - 16 q^{9} + 8 q^{16} + 8 q^{24} + 8 q^{34} + 12 q^{36} - 12 q^{49} - 4 q^{51} + 4 q^{54} - 4 q^{64} + 16 q^{81} - 8 q^{91} + 8 q^{94} - 12 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2175, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2175.1.b.a $2$ $1.085$ $$\Q(\sqrt{-1})$$ $D_{3}$ $$\Q(\sqrt{-87})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{6}-iq^{7}-iq^{8}+\cdots$$
2175.1.b.b $2$ $1.085$ $$\Q(\sqrt{-1})$$ $D_{3}$ $$\Q(\sqrt{-87})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{6}+iq^{7}-iq^{8}+\cdots$$
2175.1.b.c $6$ $1.085$ 6.0.419904.1 $D_{9}$ $$\Q(\sqrt{-87})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}-\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$
2175.1.b.d $6$ $1.085$ 6.0.419904.1 $D_{9}$ $$\Q(\sqrt{-87})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(2175, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(2175, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(435, [\chi])$$$$^{\oplus 2}$$