Properties

 Label 182.2.e Level $182$ Weight $2$ Character orbit 182.e Rep. character $\chi_{182}(107,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $20$ Newform subspaces $4$ Sturm bound $56$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$182 = 2 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 182.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$4$$ Sturm bound: $$56$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(182, [\chi])$$.

Total New Old
Modular forms 64 20 44
Cusp forms 48 20 28
Eisenstein series 16 0 16

Trace form

 $$20q - 2q^{3} + 20q^{4} - 6q^{7} - 8q^{9} + O(q^{10})$$ $$20q - 2q^{3} + 20q^{4} - 6q^{7} - 8q^{9} - 4q^{10} - 10q^{11} - 2q^{12} - 6q^{13} - 4q^{15} + 20q^{16} + 12q^{17} - 6q^{21} + 2q^{22} - 18q^{25} - 6q^{26} + 4q^{27} - 6q^{28} + 2q^{29} + 10q^{30} - 22q^{31} + 16q^{33} + 12q^{35} - 8q^{36} - 40q^{37} - 10q^{38} + 34q^{39} - 4q^{40} - 2q^{41} - 26q^{42} + 8q^{43} - 10q^{44} - 40q^{45} - 16q^{46} + 6q^{47} - 2q^{48} - 22q^{49} + 12q^{50} + 14q^{51} - 6q^{52} - 8q^{53} + 12q^{54} + 2q^{55} - 28q^{57} + 16q^{59} - 4q^{60} - 24q^{61} - 20q^{62} + 66q^{63} + 20q^{64} - 2q^{65} - 16q^{66} + 12q^{68} - 26q^{69} + 40q^{70} - 26q^{71} + 28q^{73} - 60q^{75} - 10q^{77} - 12q^{78} - 10q^{79} + 22q^{81} - 16q^{82} + 84q^{83} - 6q^{84} + 20q^{85} + 10q^{86} + 80q^{87} + 2q^{88} + 28q^{89} + 28q^{90} + 6q^{91} - 8q^{93} - 32q^{94} - 8q^{95} + 34q^{97} + 48q^{98} + 52q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(182, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
182.2.e.a $$2$$ $$1.453$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$-1$$ $$-1$$ $$4$$ $$q-q^{2}-\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$$
182.2.e.b $$2$$ $$1.453$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$-1$$ $$3$$ $$-4$$ $$q-q^{2}-\zeta_{6}q^{3}+q^{4}+3\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$$
182.2.e.c $$6$$ $$1.453$$ 6.0.4740147.1 None $$-6$$ $$1$$ $$0$$ $$-3$$ $$q-q^{2}+\beta _{4}q^{3}+q^{4}+(\beta _{4}+\beta _{5})q^{5}+\cdots$$
182.2.e.d $$10$$ $$1.453$$ 10.0.$$\cdots$$.1 None $$10$$ $$-1$$ $$-2$$ $$-3$$ $$q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{5}q^{6}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(182, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(182, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 2}$$