# Properties

 Label 104.2.o Level $104$ Weight $2$ Character orbit 104.o Rep. character $\chi_{104}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ 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.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ 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 36 8 28
Cusp forms 20 8 12
Eisenstein series 16 0 16

## Trace form

 $$8 q + 2 q^{3} - 6 q^{7} - 6 q^{9} + O(q^{10})$$ $$8 q + 2 q^{3} - 6 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} - 6 q^{19} + 2 q^{23} - 20 q^{25} - 28 q^{27} - 8 q^{29} + 6 q^{33} + 16 q^{35} - 24 q^{37} - 14 q^{39} + 12 q^{41} + 6 q^{43} + 30 q^{45} + 2 q^{49} + 68 q^{51} + 20 q^{53} + 16 q^{55} + 18 q^{59} - 4 q^{61} + 36 q^{63} + 14 q^{65} - 42 q^{67} - 18 q^{69} - 54 q^{71} - 22 q^{75} - 60 q^{77} + 16 q^{79} - 20 q^{81} + 6 q^{85} - 10 q^{87} - 18 q^{89} - 46 q^{91} + 36 q^{93} + 16 q^{95} + 30 q^{97} + O(q^{100})$$

## 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.o.a $8$ $0.830$ 8.0.195105024.2 None $$0$$ $$2$$ $$0$$ $$-6$$ $$q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(104, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 2}$$