# Properties

 Label 4020.2.q Level 4020 Weight 2 Character orbit q Rep. character $$\chi_{4020}(841,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 92 Newform subspaces 13 Sturm bound 1632 Trace bound 11

# Related objects

## Defining parameters

 Level: $$N$$ = $$4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4020.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$67$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$13$$ Sturm bound: $$1632$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4020, [\chi])$$.

Total New Old
Modular forms 1656 92 1564
Cusp forms 1608 92 1516
Eisenstein series 48 0 48

## Trace form

 $$92q + 4q^{3} - 4q^{7} + 92q^{9} + O(q^{10})$$ $$92q + 4q^{3} - 4q^{7} + 92q^{9} - 4q^{11} - 10q^{13} + 8q^{17} - 4q^{21} + 12q^{23} + 92q^{25} + 4q^{27} + 20q^{29} - 2q^{31} - 4q^{35} - 4q^{37} + 2q^{39} + 4q^{41} - 20q^{43} - 20q^{47} - 50q^{49} + 4q^{51} - 16q^{53} + 12q^{55} - 16q^{57} - 56q^{59} + 10q^{61} - 4q^{63} + 8q^{65} - 46q^{67} - 8q^{69} - 8q^{71} + 10q^{73} + 4q^{75} + 8q^{77} - 10q^{79} + 92q^{81} - 4q^{83} - 12q^{85} + 4q^{87} + 64q^{89} - 8q^{91} - 14q^{93} - 30q^{97} - 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4020, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4020.2.q.a $$2$$ $$32.100$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$2$$ $$-3$$ $$q-q^{3}+q^{5}-3\zeta_{6}q^{7}+q^{9}-5\zeta_{6}q^{11}+\cdots$$
4020.2.q.b $$2$$ $$32.100$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$2$$ $$-3$$ $$q-q^{3}+q^{5}-3\zeta_{6}q^{7}+q^{9}+5\zeta_{6}q^{11}+\cdots$$
4020.2.q.c $$2$$ $$32.100$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$2$$ $$1$$ $$q-q^{3}+q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots$$
4020.2.q.d $$2$$ $$32.100$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$2$$ $$1$$ $$q-q^{3}+q^{5}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+\cdots$$
4020.2.q.e $$2$$ $$32.100$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$-1$$ $$q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots$$
4020.2.q.f $$2$$ $$32.100$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$-1$$ $$q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+\cdots$$
4020.2.q.g $$2$$ $$32.100$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$-1$$ $$q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}+5\zeta_{6}q^{11}+\cdots$$
4020.2.q.h $$2$$ $$32.100$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$1$$ $$q+q^{3}-q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots$$
4020.2.q.i $$4$$ $$32.100$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$4$$ $$-4$$ $$-1$$ $$q+q^{3}-q^{5}+(-\beta _{1}+\beta _{3})q^{7}+q^{9}+\cdots$$
4020.2.q.j $$12$$ $$32.100$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$12$$ $$-12$$ $$2$$ $$q+q^{3}-q^{5}+(\beta _{1}-\beta _{6}-\beta _{9})q^{7}+q^{9}+\cdots$$
4020.2.q.k $$14$$ $$32.100$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$-14$$ $$14$$ $$3$$ $$q-q^{3}+q^{5}-\beta _{6}q^{7}+q^{9}+(1-\beta _{5}+\cdots)q^{11}+\cdots$$
4020.2.q.l $$22$$ $$32.100$$ None $$0$$ $$-22$$ $$-22$$ $$1$$
4020.2.q.m $$24$$ $$32.100$$ None $$0$$ $$24$$ $$24$$ $$-3$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4020, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4020, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(67, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(134, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(201, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(268, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(335, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(402, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(670, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(804, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1005, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1340, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2010, [\chi])$$$$^{\oplus 2}$$