# Properties

 Label 104.2.f Level $104$ Weight $2$ Character orbit 104.f Rep. character $\chi_{104}(25,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $28$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$104 = 2^{3} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 104.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$28$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(104, [\chi])$$.

Total New Old
Modular forms 18 4 14
Cusp forms 10 4 6
Eisenstein series 8 0 8

## Trace form

 $$4 q - 2 q^{3} + 6 q^{9} + O(q^{10})$$ $$4 q - 2 q^{3} + 6 q^{9} - 6 q^{13} - 6 q^{17} + 4 q^{23} + 2 q^{25} - 14 q^{27} - 4 q^{29} - 22 q^{35} + 20 q^{39} + 30 q^{43} - 14 q^{49} - 14 q^{51} + 16 q^{53} + 32 q^{55} + 28 q^{61} - 14 q^{65} - 36 q^{69} + 16 q^{75} + 24 q^{77} - 28 q^{79} - 28 q^{81} - 32 q^{87} - 2 q^{91} - 4 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(104, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
104.2.f.a $4$ $0.830$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+\beta _{3})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(104, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(104, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 3}$$