Properties

 Label 5520.2.be Level $5520$ Weight $2$ Character orbit 5520.be Rep. character $\chi_{5520}(1471,\cdot)$ Character field $\Q$ Dimension $96$ Newform subspaces $4$ Sturm bound $2304$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5520.be (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$92$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$2304$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(5520, [\chi])$$.

Total New Old
Modular forms 1176 96 1080
Cusp forms 1128 96 1032
Eisenstein series 48 0 48

Trace form

 $$96q - 96q^{9} + O(q^{10})$$ $$96q - 96q^{9} - 96q^{25} + 48q^{41} + 144q^{49} + 96q^{81} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(5520, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
5520.2.be.a $$16$$ $$44.077$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{10}q^{3}+\beta _{10}q^{5}+(-1-\beta _{4})q^{7}+\cdots$$
5520.2.be.b $$16$$ $$44.077$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{10}q^{3}+\beta _{10}q^{5}+(1+\beta _{4})q^{7}-q^{9}+\cdots$$
5520.2.be.c $$32$$ $$44.077$$ None $$0$$ $$0$$ $$0$$ $$-8$$
5520.2.be.d $$32$$ $$44.077$$ None $$0$$ $$0$$ $$0$$ $$8$$

Decomposition of $$S_{2}^{\mathrm{old}}(5520, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(5520, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(92, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(276, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(368, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(460, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1104, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1380, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1840, [\chi])$$$$^{\oplus 2}$$