# Properties

 Label 102.2.b Level $102$ Weight $2$ Character orbit 102.b Rep. character $\chi_{102}(67,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $36$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$102 = 2 \cdot 3 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 102.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(102, [\chi])$$.

Total New Old
Modular forms 22 2 20
Cusp forms 14 2 12
Eisenstein series 8 0 8

## Trace form

 $$2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9} + O(q^{10})$$ $$2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9} - 12 q^{13} + 4 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{21} + 2 q^{25} - 12 q^{26} + 4 q^{30} + 2 q^{32} - 2 q^{34} + 8 q^{35} - 2 q^{36} - 4 q^{42} + 8 q^{43} + 16 q^{47} + 6 q^{49} + 2 q^{50} + 8 q^{51} - 12 q^{52} - 12 q^{53} + 4 q^{60} + 2 q^{64} + 16 q^{67} - 2 q^{68} + 12 q^{69} + 8 q^{70} - 2 q^{72} + 2 q^{81} - 32 q^{83} - 4 q^{84} - 16 q^{85} + 8 q^{86} - 12 q^{87} + 20 q^{89} - 20 q^{93} + 16 q^{94} + 6 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(102, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
102.2.b.a $2$ $0.814$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+iq^{3}+q^{4}-2iq^{5}+iq^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(102, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(102, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(51, [\chi])$$$$^{\oplus 2}$$