# Properties

 Label 102.2.h Level 102 Weight 2 Character orbit h Rep. character $$\chi_{102}(19,\cdot)$$ Character field $$\Q(\zeta_{8})$$ Dimension 16 Newforms 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: $$\Q(\zeta_{8})$$ Newforms: $$2$$ 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

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

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

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

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