# Properties

 Label 1775.1.d Level $1775$ Weight $1$ Character orbit 1775.d Rep. character $\chi_{1775}(851,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $3$ Sturm bound $180$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1775 = 5^{2} \cdot 71$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1775.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$71$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$180$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1775, [\chi])$$.

Total New Old
Modular forms 25 13 12
Cusp forms 19 10 9
Eisenstein series 6 3 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 10 0 0 0

## Trace form

 $$10 q + q^{2} + q^{3} + 9 q^{4} - 2 q^{6} + 2 q^{8} + 9 q^{9} + O(q^{10})$$ $$10 q + q^{2} + q^{3} + 9 q^{4} - 2 q^{6} + 2 q^{8} + 9 q^{9} + 3 q^{12} + 8 q^{16} - 4 q^{18} - q^{19} - 11 q^{24} + 2 q^{27} - q^{29} + 3 q^{32} + 6 q^{36} + q^{37} - 5 q^{38} + q^{43} - 2 q^{48} + 10 q^{49} - 4 q^{54} + 2 q^{57} + 2 q^{58} + 7 q^{64} - 4 q^{71} - q^{72} + q^{73} - 9 q^{74} - 3 q^{76} - q^{79} + 8 q^{81} + q^{83} - 2 q^{86} - 5 q^{87} - q^{89} - 13 q^{96} + q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1775, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1775.1.d.a $1$ $0.886$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-71})$$, $$\Q(\sqrt{-355})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-q^{4}-q^{9}+q^{16}+2q^{19}+2q^{29}+\cdots$$
1775.1.d.b $3$ $0.886$ $$\Q(\zeta_{14})^+$$ $D_{7}$ $$\Q(\sqrt{-71})$$ None $$1$$ $$1$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
1775.1.d.c $6$ $0.886$ $$\Q(\zeta_{28})^+$$ $D_{14}$ $$\Q(\sqrt{-71})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(1-2\beta _{2}+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1775, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1775, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(71, [\chi])$$$$^{\oplus 3}$$