Properties

 Label 21.3.h Level $21$ Weight $3$ Character orbit 21.h Rep. character $\chi_{21}(2,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $6$ Newform subspaces $2$ Sturm bound $8$ Trace bound $1$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$21 = 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 21.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$8$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(21, [\chi])$$.

Total New Old
Modular forms 14 14 0
Cusp forms 6 6 0
Eisenstein series 8 8 0

Trace form

 $$6 q - q^{3} - 2 q^{4} - 20 q^{6} + q^{7} - 7 q^{9} + O(q^{10})$$ $$6 q - q^{3} - 2 q^{4} - 20 q^{6} + q^{7} - 7 q^{9} - 10 q^{10} + 16 q^{12} + 38 q^{13} + 20 q^{15} + 22 q^{16} + 40 q^{18} - 43 q^{19} + 22 q^{21} - 100 q^{22} + 30 q^{24} - 65 q^{25} - 142 q^{27} - 6 q^{28} - 20 q^{30} + 19 q^{31} + 50 q^{33} + 240 q^{34} + 76 q^{36} + 49 q^{37} + 77 q^{39} - 30 q^{40} - 70 q^{42} + 54 q^{43} - 40 q^{45} - 60 q^{46} - 248 q^{48} - 27 q^{49} - 120 q^{51} - 96 q^{52} + 70 q^{54} + 100 q^{55} + 62 q^{57} - 70 q^{58} + 10 q^{60} - 22 q^{61} + 127 q^{63} - 36 q^{64} + 100 q^{66} - 91 q^{67} + 120 q^{69} + 70 q^{70} + 120 q^{72} + 61 q^{73} - 5 q^{75} + 24 q^{76} + 40 q^{78} + 147 q^{79} + 77 q^{81} - 140 q^{82} - 76 q^{84} - 240 q^{85} - 70 q^{87} + 150 q^{88} - 20 q^{90} - 327 q^{91} - 27 q^{93} + 60 q^{94} - 70 q^{96} - 368 q^{97} - 400 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(21, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.3.h.a $2$ $0.572$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$-13$$ $$q+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots$$
21.3.h.b $4$ $0.572$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None $$0$$ $$-4$$ $$0$$ $$14$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$$