# Properties

 Label 2520.2.bi Level $2520$ Weight $2$ Character orbit 2520.bi Rep. character $\chi_{2520}(361,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $80$ Newform subspaces $19$ Sturm bound $1152$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2520.bi (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$19$$ Sturm bound: $$1152$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2520, [\chi])$$.

Total New Old
Modular forms 1216 80 1136
Cusp forms 1088 80 1008
Eisenstein series 128 0 128

## Trace form

 $$80q + 2q^{5} - 4q^{7} + O(q^{10})$$ $$80q + 2q^{5} - 4q^{7} + 2q^{11} + 12q^{17} + 6q^{19} - 40q^{25} - 20q^{29} - 8q^{31} - 2q^{35} - 4q^{37} + 16q^{41} - 12q^{47} - 42q^{49} - 20q^{53} - 4q^{59} - 14q^{61} - 6q^{65} + 12q^{67} + 64q^{71} - 4q^{73} + 48q^{77} + 56q^{83} + 26q^{89} + 28q^{91} - 4q^{95} + 48q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2520, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2520.2.bi.a $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-5$$ $$q-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$$
2520.2.bi.b $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-4$$ $$q-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$$
2520.2.bi.c $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$1$$ $$q-\zeta_{6}q^{5}+(2-3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
2520.2.bi.d $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$1$$ $$q-\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
2520.2.bi.e $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$4$$ $$q-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$$
2520.2.bi.f $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$5$$ $$q-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots$$
2520.2.bi.g $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-5$$ $$q+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-q^{13}+(2+\cdots)q^{17}+\cdots$$
2520.2.bi.h $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-1$$ $$q+\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots$$
2520.2.bi.i $$2$$ $$20.122$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$4$$ $$q+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$$
2520.2.bi.j $$4$$ $$20.122$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots$$
2520.2.bi.k $$4$$ $$20.122$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-2$$ $$q-\beta _{2}q^{5}+(-1-\beta _{1}-\beta _{2}-2\beta _{3})q^{7}+\cdots$$
2520.2.bi.l $$4$$ $$20.122$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-2$$ $$q-\beta _{2}q^{5}+(\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\beta _{1}q^{11}+\cdots$$
2520.2.bi.m $$6$$ $$20.122$$ 6.0.4406832.1 None $$0$$ $$0$$ $$-3$$ $$-1$$ $$q+(-1+\beta _{4})q^{5}+(-\beta _{2}-\beta _{5})q^{7}+(\beta _{4}+\cdots)q^{11}+\cdots$$
2520.2.bi.n $$6$$ $$20.122$$ 6.0.29428272.1 None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(-1-\beta _{3})q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots$$
2520.2.bi.o $$6$$ $$20.122$$ 6.0.38363328.2 None $$0$$ $$0$$ $$3$$ $$-2$$ $$q-\beta _{3}q^{5}+(-\beta _{1}+\beta _{4})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$$
2520.2.bi.p $$6$$ $$20.122$$ 6.0.4406832.1 None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+(1-\beta _{4})q^{5}+(-\beta _{2}-\beta _{5})q^{7}+(-\beta _{4}+\cdots)q^{11}+\cdots$$
2520.2.bi.q $$6$$ $$20.122$$ 6.0.11337408.1 None $$0$$ $$0$$ $$3$$ $$6$$ $$q+\beta _{2}q^{5}+(1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{7}+\cdots$$
2520.2.bi.r $$10$$ $$20.122$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$-5$$ $$-1$$ $$q+\beta _{1}q^{5}+\beta _{6}q^{7}+\beta _{3}q^{11}+(\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots$$
2520.2.bi.s $$10$$ $$20.122$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$5$$ $$-1$$ $$q-\beta _{1}q^{5}+\beta _{6}q^{7}-\beta _{3}q^{11}+(\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2520, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2520, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(840, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1260, [\chi])$$$$^{\oplus 2}$$