Properties

 Label 76.3.b Level $76$ Weight $3$ Character orbit 76.b Rep. character $\chi_{76}(39,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $2$ Sturm bound $30$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 76.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$30$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

Dimensions

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

Total New Old
Modular forms 22 18 4
Cusp forms 18 18 0
Eisenstein series 4 0 4

Trace form

 $$18 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 6 q^{6} - 8 q^{8} - 54 q^{9} + O(q^{10})$$ $$18 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 6 q^{6} - 8 q^{8} - 54 q^{9} - 8 q^{10} + 16 q^{12} + 12 q^{13} + 36 q^{14} + 26 q^{16} + 20 q^{17} + 22 q^{18} + 40 q^{20} - 16 q^{21} - 24 q^{22} - 98 q^{24} + 46 q^{25} + 26 q^{26} + 6 q^{28} - 4 q^{29} - 84 q^{30} + 8 q^{32} - 48 q^{33} - 68 q^{34} + 68 q^{36} + 76 q^{37} - 180 q^{40} + 100 q^{41} + 202 q^{42} + 24 q^{44} - 68 q^{45} + 52 q^{46} + 248 q^{48} - 46 q^{49} - 190 q^{50} - 204 q^{52} + 12 q^{53} - 146 q^{54} + 12 q^{56} - 14 q^{58} - 52 q^{60} - 100 q^{61} + 300 q^{62} + 138 q^{64} - 88 q^{65} + 36 q^{66} + 58 q^{68} - 160 q^{69} + 36 q^{70} + 192 q^{72} - 268 q^{73} - 200 q^{74} + 296 q^{77} + 508 q^{78} - 316 q^{80} + 242 q^{81} - 276 q^{82} - 260 q^{84} + 176 q^{85} - 268 q^{86} + 472 q^{88} + 20 q^{89} + 316 q^{90} + 114 q^{92} + 80 q^{93} - 376 q^{94} - 10 q^{96} + 260 q^{97} - 106 q^{98} + O(q^{100})$$

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.b.a $4$ $2.071$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$-4$$ $$0$$ $$-4$$ $$0$$ $$q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots$$
76.3.b.b $14$ $2.071$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots$$