Properties

 Label 76.3.g Level $76$ Weight $3$ Character orbit 76.g Rep. character $\chi_{76}(7,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $36$ Newform subspaces $3$ Sturm bound $30$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 76.g (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$76$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$30$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(76, [\chi])$$.

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

 $$36q - q^{2} - 3q^{4} - 2q^{5} - 15q^{6} + 2q^{8} + 36q^{9} + O(q^{10})$$ $$36q - q^{2} - 3q^{4} - 2q^{5} - 15q^{6} + 2q^{8} + 36q^{9} + 8q^{10} - 22q^{12} + 6q^{13} + 18q^{14} + 13q^{16} - 26q^{17} - 28q^{18} - 76q^{20} - 8q^{21} + 33q^{22} + 17q^{24} - 52q^{25} - 104q^{26} - 42q^{28} - 2q^{29} - 96q^{30} + 19q^{32} + 36q^{33} + 44q^{34} - 2q^{36} - 88q^{37} - 186q^{38} + 30q^{40} + 50q^{41} + 86q^{42} + 225q^{44} + 56q^{45} + 212q^{46} - 113q^{48} - 92q^{49} + 418q^{50} - 54q^{52} + 6q^{53} + 167q^{54} + 276q^{56} - 6q^{57} + 80q^{58} - 182q^{60} - 146q^{61} - 156q^{62} + 438q^{64} - 164q^{65} - 45q^{66} + 140q^{68} - 428q^{69} + 36q^{70} - 294q^{72} - 134q^{73} - 232q^{74} + 483q^{76} + 352q^{77} + 152q^{78} - 110q^{80} + 334q^{81} - 357q^{82} - 100q^{84} + 346q^{85} + 22q^{86} - 718q^{88} + 118q^{89} - 64q^{90} - 540q^{92} + 184q^{93} - 488q^{94} - 506q^{96} - 374q^{97} + 271q^{98} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(76, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
76.3.g.a $$4$$ $$2.071$$ $$\Q(\sqrt{-3}, \sqrt{-10})$$ None $$-4$$ $$6$$ $$-4$$ $$0$$ $$q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots$$
76.3.g.b $$4$$ $$2.071$$ $$\Q(\sqrt{-3}, \sqrt{-10})$$ None $$8$$ $$-6$$ $$-4$$ $$0$$ $$q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots$$
76.3.g.c $$28$$ $$2.071$$ None $$-5$$ $$0$$ $$6$$ $$0$$