# Properties

 Label 104.1.h Level $104$ Weight $1$ Character orbit 104.h Rep. character $\chi_{104}(51,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $2$ Sturm bound $14$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$104 = 2^{3} \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 104.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$104$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$14$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(104, [\chi])$$.

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q - 2 q^{3} + 2 q^{4} + O(q^{10})$$ $$2 q - 2 q^{3} + 2 q^{4} - 2 q^{10} - 2 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{26} + 2 q^{27} + 2 q^{30} + 2 q^{35} - 2 q^{40} + 2 q^{42} - 2 q^{43} - 2 q^{48} + 2 q^{51} - 2 q^{56} + 4 q^{62} + 2 q^{64} - 2 q^{65} - 2 q^{68} - 2 q^{74} - 2 q^{78} - 2 q^{81} - 2 q^{91} - 2 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(104, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
104.1.h.a $1$ $0.052$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-26})$$ None $$-1$$ $$-1$$ $$1$$ $$1$$ $$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$$
104.1.h.b $1$ $0.052$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-26})$$ None $$1$$ $$-1$$ $$-1$$ $$-1$$ $$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$$