# Properties

 Label 1700.1.h Level $1700$ Weight $1$ Character orbit 1700.h Rep. character $\chi_{1700}(951,\cdot)$ Character field $\Q$ Dimension $9$ Newform subspaces $7$ Sturm bound $270$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1700 = 2^{2} \cdot 5^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1700.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$68$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$270$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1700, [\chi])$$.

Total New Old
Modular forms 24 15 9
Cusp forms 12 9 3
Eisenstein series 12 6 6

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 9 0 0 0

## Trace form

 $$9 q + q^{2} + 9 q^{4} + q^{8} + 7 q^{9} + O(q^{10})$$ $$9 q + q^{2} + 9 q^{4} + q^{8} + 7 q^{9} + 2 q^{13} + 9 q^{16} - q^{17} - q^{18} - 8 q^{21} - 6 q^{26} + q^{32} - q^{34} + 7 q^{36} + 7 q^{49} + 2 q^{52} - 2 q^{53} + 9 q^{64} - 8 q^{66} - q^{68} - 8 q^{69} - q^{72} + q^{81} - 8 q^{84} - 2 q^{89} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1700, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1700.1.h.a $1$ $0.848$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-17})$$ None $$-1$$ $$-1$$ $$0$$ $$-1$$ $$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$$
1700.1.h.b $1$ $0.848$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-17})$$ None $$-1$$ $$1$$ $$0$$ $$1$$ $$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$$
1700.1.h.c $1$ $0.848$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-17})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$$
1700.1.h.d $1$ $0.848$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-17})$$ $$\Q(\sqrt{17})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}+q^{8}-q^{9}+2q^{13}+q^{16}+\cdots$$
1700.1.h.e $1$ $0.848$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-17})$$ None $$1$$ $$1$$ $$0$$ $$1$$ $$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$$
1700.1.h.f $2$ $0.848$ $$\Q(\sqrt{3})$$ $D_{6}$ $$\Q(\sqrt{-17})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots$$
1700.1.h.g $2$ $0.848$ $$\Q(\sqrt{3})$$ $D_{6}$ $$\Q(\sqrt{-17})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{8}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1700, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1700, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(340, [\chi])$$$$^{\oplus 2}$$