# Properties

 Label 82.2.c Level $82$ Weight $2$ Character orbit 82.c Rep. character $\chi_{82}(9,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $6$ Newform subspaces $3$ Sturm bound $21$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$82 = 2 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 82.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$41$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$21$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(82, [\chi])$$.

Total New Old
Modular forms 26 6 20
Cusp forms 18 6 12
Eisenstein series 8 0 8

## Trace form

 $$6q + 2q^{3} - 6q^{4} - 6q^{6} + O(q^{10})$$ $$6q + 2q^{3} - 6q^{4} - 6q^{6} - 4q^{10} - 10q^{11} - 2q^{12} + 16q^{13} + 4q^{15} + 6q^{16} + 10q^{17} - 6q^{18} - 10q^{19} + 14q^{22} - 8q^{23} + 6q^{24} + 6q^{25} - 16q^{27} - 4q^{29} + 12q^{30} - 16q^{31} - 2q^{34} - 24q^{35} + 12q^{37} + 2q^{38} + 4q^{40} - 24q^{41} + 24q^{42} + 10q^{44} + 28q^{45} + 16q^{47} + 2q^{48} - 36q^{51} - 16q^{52} - 8q^{53} + 12q^{55} + 12q^{57} - 4q^{58} - 28q^{59} - 4q^{60} + 48q^{63} - 6q^{64} + 32q^{65} + 12q^{66} - 14q^{67} - 10q^{68} - 16q^{69} - 24q^{70} + 20q^{71} + 6q^{72} + 2q^{75} + 10q^{76} - 48q^{78} + 16q^{79} - 10q^{81} - 10q^{82} + 24q^{83} + 20q^{85} + 8q^{86} - 14q^{88} - 10q^{89} + 8q^{92} + 8q^{93} - 16q^{94} + 4q^{95} - 6q^{96} + 6q^{97} - 58q^{98} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(82, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
82.2.c.a $$2$$ $$0.655$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}+(-1+i)q^{3}-q^{4}+2iq^{5}+\cdots$$
82.2.c.b $$2$$ $$0.655$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$6$$ $$q-iq^{2}-q^{4}-2iq^{5}+(3-3i)q^{7}+\cdots$$
82.2.c.c $$2$$ $$0.655$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$0$$ $$-6$$ $$q-iq^{2}+(2-2i)q^{3}-q^{4}+2iq^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(82, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(82, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(41, [\chi])$$$$^{\oplus 2}$$