# Properties

 Label 102.2.f Level $102$ Weight $2$ Character orbit 102.f Rep. character $\chi_{102}(13,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ 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.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q(i)$$ 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 44 4 40
Cusp forms 28 4 24
Eisenstein series 16 0 16

## Trace form

 $$4 q - 4 q^{4} - 4 q^{5} + 8 q^{7} + O(q^{10})$$ $$4 q - 4 q^{4} - 4 q^{5} + 8 q^{7} - 4 q^{10} - 8 q^{14} + 4 q^{16} - 12 q^{17} + 4 q^{18} + 4 q^{20} + 8 q^{21} + 8 q^{23} - 8 q^{28} + 4 q^{29} + 8 q^{30} + 8 q^{31} - 16 q^{33} - 12 q^{37} + 16 q^{38} - 8 q^{39} + 4 q^{40} - 20 q^{41} + 4 q^{45} - 8 q^{46} + 16 q^{47} + 4 q^{50} + 8 q^{51} - 32 q^{55} + 8 q^{56} - 8 q^{57} + 4 q^{58} + 20 q^{61} + 8 q^{62} + 8 q^{63} - 4 q^{64} - 16 q^{65} + 16 q^{67} + 12 q^{68} - 24 q^{69} + 24 q^{71} - 4 q^{72} + 4 q^{73} - 12 q^{74} + 16 q^{75} - 8 q^{78} - 24 q^{79} - 4 q^{80} - 4 q^{81} + 20 q^{82} - 8 q^{84} + 28 q^{85} - 16 q^{86} - 4 q^{90} - 16 q^{91} - 8 q^{92} - 4 q^{97} - 20 q^{98} + O(q^{100})$$

## 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.f.a $4$ $0.814$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-4$$ $$8$$ $$q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots$$

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

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