# Properties

 Label 102.2.h Level $102$ Weight $2$ Character orbit 102.h Rep. character $\chi_{102}(19,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $16$ Newform subspaces $2$ Sturm bound $36$ Trace bound $10$

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## Defining parameters

 Level: $$N$$ $$=$$ $$102 = 2 \cdot 3 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 102.h (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 88 16 72
Cusp forms 56 16 40
Eisenstein series 32 0 32

## Trace form

 $$16 q + 16 q^{5} + O(q^{10})$$ $$16 q + 16 q^{5} - 16 q^{11} - 16 q^{14} - 16 q^{16} - 16 q^{19} - 16 q^{22} - 16 q^{23} - 16 q^{25} + 16 q^{26} + 16 q^{28} + 16 q^{34} - 32 q^{35} + 16 q^{37} - 16 q^{39} + 16 q^{41} + 16 q^{42} + 16 q^{44} + 32 q^{50} + 48 q^{53} + 32 q^{57} + 16 q^{59} - 16 q^{61} + 64 q^{65} + 16 q^{66} + 32 q^{67} + 16 q^{69} + 16 q^{70} - 48 q^{71} + 16 q^{73} - 16 q^{74} - 32 q^{75} + 16 q^{76} - 64 q^{77} - 32 q^{78} + 16 q^{79} - 16 q^{80} - 16 q^{83} - 16 q^{84} - 48 q^{85} - 32 q^{86} - 48 q^{87} - 16 q^{88} + 48 q^{91} - 16 q^{93} - 16 q^{94} + 16 q^{95} - 16 q^{99} + O(q^{100})$$

## 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.h.a $8$ $0.814$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots$$
102.2.h.b $8$ $0.814$ $$\Q(\zeta_{16})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\zeta_{16}^{6}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}+(1+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(102, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(17, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(51, [\chi])$$$$^{\oplus 2}$$