# Properties

 Label 880.2.bo Level $880$ Weight $2$ Character orbit 880.bo Rep. character $\chi_{880}(81,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $96$ Newform subspaces $11$ Sturm bound $288$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$880 = 2^{4} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 880.bo (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$11$$ Sturm bound: $$288$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(880, [\chi])$$.

Total New Old
Modular forms 624 96 528
Cusp forms 528 96 432
Eisenstein series 96 0 96

## Trace form

 $$96 q + 4 q^{7} - 16 q^{9} + O(q^{10})$$ $$96 q + 4 q^{7} - 16 q^{9} + 4 q^{11} + 8 q^{17} + 8 q^{23} - 24 q^{25} - 16 q^{29} - 20 q^{33} - 12 q^{35} + 24 q^{37} + 36 q^{39} - 20 q^{41} + 56 q^{43} + 36 q^{47} - 36 q^{49} + 36 q^{51} + 40 q^{53} - 20 q^{57} - 16 q^{59} + 16 q^{61} + 20 q^{63} + 8 q^{65} + 40 q^{67} + 32 q^{69} - 28 q^{71} + 24 q^{73} - 24 q^{77} - 84 q^{79} - 68 q^{81} - 36 q^{83} - 168 q^{87} - 16 q^{89} - 64 q^{91} + 32 q^{93} + 16 q^{95} - 28 q^{97} - 112 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(880, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
880.2.bo.a $4$ $7.027$ $$\Q(\zeta_{10})$$ None $$0$$ $$-4$$ $$1$$ $$-1$$ $$q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+\zeta_{10}q^{5}+\cdots$$
880.2.bo.b $4$ $7.027$ $$\Q(\zeta_{10})$$ None $$0$$ $$-4$$ $$1$$ $$0$$ $$q+(-\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\zeta_{10}q^{5}+\cdots$$
880.2.bo.c $8$ $7.027$ 8.0.159390625.1 None $$0$$ $$-5$$ $$-2$$ $$1$$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{3}+\cdots$$
880.2.bo.d $8$ $7.027$ 8.0.13140625.1 None $$0$$ $$-1$$ $$-2$$ $$-1$$ $$q+(-\beta _{1}+\beta _{5})q^{3}+\beta _{7}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$$
880.2.bo.e $8$ $7.027$ 8.0.159390625.1 None $$0$$ $$-1$$ $$-2$$ $$3$$ $$q-\beta _{1}q^{3}-\beta _{6}q^{5}+(2-3\beta _{2}-3\beta _{3}+\cdots)q^{7}+\cdots$$
880.2.bo.f $8$ $7.027$ 8.0.26265625.1 None $$0$$ $$1$$ $$2$$ $$-1$$ $$q+(\beta _{1}+\beta _{7})q^{3}+\beta _{2}q^{5}+(1-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$$
880.2.bo.g $8$ $7.027$ 8.0.682515625.5 None $$0$$ $$4$$ $$-2$$ $$1$$ $$q+(-\beta _{1}-\beta _{3}+\beta _{5}+\beta _{6}+\beta _{7})q^{3}+\cdots$$
880.2.bo.h $8$ $7.027$ 8.0.13140625.1 None $$0$$ $$5$$ $$2$$ $$1$$ $$q+(1-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{5}+\beta _{6})q^{3}+\cdots$$
880.2.bo.i $12$ $7.027$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$1$$ $$3$$ $$1$$ $$q+(-\beta _{3}-\beta _{8})q^{3}-\beta _{6}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$$
880.2.bo.j $12$ $7.027$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$1$$ $$3$$ $$8$$ $$q+(-\beta _{1}-\beta _{5})q^{3}+\beta _{8}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$$
880.2.bo.k $16$ $7.027$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$3$$ $$-4$$ $$-8$$ $$q+\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(880, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(880, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(44, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(88, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(176, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(220, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(440, [\chi])$$$$^{\oplus 2}$$