Properties

 Label 420.2.q Level $420$ Weight $2$ Character orbit 420.q Rep. character $\chi_{420}(121,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $12$ Newform subspaces $4$ Sturm bound $192$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$420 = 2^{2} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 420.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$4$$ Sturm bound: $$192$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$11$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(420, [\chi])$$.

Total New Old
Modular forms 216 12 204
Cusp forms 168 12 156
Eisenstein series 48 0 48

Trace form

 $$12q - 2q^{3} - 2q^{7} - 6q^{9} + O(q^{10})$$ $$12q - 2q^{3} - 2q^{7} - 6q^{9} + 4q^{11} + 12q^{13} + 8q^{17} + 6q^{19} + 4q^{21} - 6q^{25} + 4q^{27} - 8q^{29} - 2q^{31} - 8q^{33} + 18q^{37} + 10q^{39} - 24q^{41} - 4q^{43} - 8q^{47} + 18q^{49} - 12q^{51} + 8q^{55} - 20q^{57} + 4q^{59} + 12q^{61} - 2q^{63} + 4q^{65} - 6q^{67} - 8q^{69} + 48q^{71} - 26q^{73} - 2q^{75} - 36q^{77} - 14q^{79} - 6q^{81} - 56q^{83} + 8q^{85} + 16q^{89} + 22q^{91} + 2q^{93} - 16q^{95} + 64q^{97} - 8q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(420, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
420.2.q.a $$2$$ $$3.354$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$5$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
420.2.q.b $$2$$ $$3.354$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
420.2.q.c $$4$$ $$3.354$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$-2$$ $$-2$$ $$0$$ $$q+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+\beta _{1}q^{7}+(-1+\cdots)q^{9}+\cdots$$
420.2.q.d $$4$$ $$3.354$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$2$$ $$-2$$ $$q+(-1-\beta _{1})q^{3}-\beta _{1}q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(420, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(420, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$