# Properties

 Label 7524.2.l Level 7524 Weight 2 Character orbit l Rep. character $$\chi_{7524}(2089,\cdot)$$ Character field $$\Q$$ Dimension 100 Newforms 6 Sturm bound 2880 Trace bound 25

# Related objects

## Defining parameters

 Level: $$N$$ = $$7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 7524.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$209$$ Character field: $$\Q$$ Newforms: $$6$$ Sturm bound: $$2880$$ Trace bound: $$25$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(7524, [\chi])$$.

Total New Old
Modular forms 1464 100 1364
Cusp forms 1416 100 1316
Eisenstein series 48 0 48

## Trace form

 $$100q + 2q^{5} + O(q^{10})$$ $$100q + 2q^{5} - q^{11} + 8q^{23} + 106q^{25} - 2q^{47} - 78q^{49} - 5q^{55} + 53q^{77} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(7524, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
7524.2.l.a $$4$$ $$60.079$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots$$
7524.2.l.b $$8$$ $$60.079$$ 8.0.$$\cdots$$.6 $$\Q(\sqrt{-627})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{11}-\beta _{1}q^{13}+\beta _{3}q^{17}-\beta _{4}q^{19}+\cdots$$
7524.2.l.c $$8$$ $$60.079$$ 8.0.2702336256.1 $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{5}+\beta _{7})q^{5}+(\beta _{3}-\beta _{4})q^{7}+(\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots$$
7524.2.l.d $$16$$ $$60.079$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{2}q^{5}+(\beta _{9}-\beta _{12})q^{7}+(-\beta _{3}-\beta _{9}+\cdots)q^{11}+\cdots$$
7524.2.l.e $$24$$ $$60.079$$ None $$0$$ $$0$$ $$0$$ $$0$$
7524.2.l.f $$40$$ $$60.079$$ None $$0$$ $$0$$ $$4$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(7524, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(7524, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(209, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(418, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(627, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(836, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1254, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1881, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2508, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(3762, [\chi])$$$$^{\oplus 2}$$