# Properties

 Label 5780.2.c Level $5780$ Weight $2$ Character orbit 5780.c Rep. character $\chi_{5780}(5201,\cdot)$ Character field $\Q$ Dimension $90$ Newform subspaces $10$ Sturm bound $1836$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5780 = 2^{2} \cdot 5 \cdot 17^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5780.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$1836$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(5780, [\chi])$$.

Total New Old
Modular forms 972 90 882
Cusp forms 864 90 774
Eisenstein series 108 0 108

## Trace form

 $$90q - 82q^{9} + O(q^{10})$$ $$90q - 82q^{9} - 4q^{15} - 16q^{19} + 32q^{21} - 90q^{25} + 20q^{33} + 8q^{35} + 16q^{43} - 36q^{47} - 94q^{49} - 48q^{53} - 16q^{55} + 12q^{59} + 4q^{67} - 24q^{69} - 24q^{77} + 58q^{81} - 8q^{83} + 72q^{87} + 36q^{89} + 52q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(5780, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
5780.2.c.a $$2$$ $$46.154$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+iq^{5}+2iq^{7}-q^{9}+2q^{13}+\cdots$$
5780.2.c.b $$2$$ $$46.154$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}-iq^{5}-2iq^{7}-q^{9}-5iq^{11}+\cdots$$
5780.2.c.c $$2$$ $$46.154$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{5}+4iq^{7}+3q^{9}-2iq^{11}-6q^{13}+\cdots$$
5780.2.c.d $$2$$ $$46.154$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{5}-2iq^{7}+3q^{9}+iq^{11}-3q^{19}+\cdots$$
5780.2.c.e $$4$$ $$46.154$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
5780.2.c.f $$6$$ $$46.154$$ 6.0.2611456.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(-2+\beta _{1}+\cdots)q^{9}+\cdots$$
5780.2.c.g $$12$$ $$46.154$$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{3}-\beta _{3}q^{5}-\beta _{6}q^{7}+\beta _{8}q^{9}+\cdots$$
5780.2.c.h $$12$$ $$46.154$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{3}-\beta _{6}q^{5}+(\beta _{7}-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots$$
5780.2.c.i $$24$$ $$46.154$$ None $$0$$ $$0$$ $$0$$ $$0$$
5780.2.c.j $$24$$ $$46.154$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(5780, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(5780, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(85, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(170, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(289, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(340, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(578, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1156, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1445, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2890, [\chi])$$$$^{\oplus 2}$$