# Properties

 Label 104.2.e Level $104$ Weight $2$ Character orbit 104.e Rep. character $\chi_{104}(77,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $3$ Sturm bound $28$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$104 = 2^{3} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 104.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$104$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$28$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

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

Total New Old
Modular forms 16 16 0
Cusp forms 12 12 0
Eisenstein series 4 4 0

## Trace form

 $$12 q - 2 q^{4} - 12 q^{9} + O(q^{10})$$ $$12 q - 2 q^{4} - 12 q^{9} - 10 q^{10} + 14 q^{12} - 6 q^{14} - 6 q^{16} - 8 q^{17} + 12 q^{22} + 8 q^{23} - 4 q^{25} - 2 q^{26} + 18 q^{30} - 36 q^{36} - 36 q^{38} + 16 q^{39} - 18 q^{40} + 34 q^{42} + 30 q^{48} + 12 q^{49} + 12 q^{52} - 56 q^{55} + 38 q^{56} + 40 q^{62} - 38 q^{64} + 16 q^{66} + 46 q^{68} - 34 q^{74} - 34 q^{78} + 16 q^{79} + 4 q^{81} - 40 q^{82} + 8 q^{87} + 48 q^{88} + 48 q^{90} - 8 q^{92} - 46 q^{94} - 16 q^{95} + O(q^{100})$$

## 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.e.a $2$ $0.830$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$2$$ $$0$$ $$q+(-1+i)q^{2}-iq^{3}-2iq^{4}+q^{5}+\cdots$$
104.2.e.b $2$ $0.830$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+(1+i)q^{2}+iq^{3}+2iq^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$$
104.2.e.c $8$ $0.830$ 8.0.4521217600.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{3}-\beta _{5}q^{4}-\beta _{6}q^{5}+\cdots$$