# Properties

 Label 1520.2.q Level $1520$ Weight $2$ Character orbit 1520.q Rep. character $\chi_{1520}(881,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $80$ Newform subspaces $16$ Sturm bound $480$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1520 = 2^{4} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1520.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$16$$ Sturm bound: $$480$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1520, [\chi])$$.

Total New Old
Modular forms 504 80 424
Cusp forms 456 80 376
Eisenstein series 48 0 48

## Trace form

 $$80 q - 4 q^{3} - 8 q^{7} - 44 q^{9} + O(q^{10})$$ $$80 q - 4 q^{3} - 8 q^{7} - 44 q^{9} + 4 q^{15} + 8 q^{17} + 12 q^{19} - 40 q^{25} + 32 q^{27} - 24 q^{31} - 12 q^{33} - 8 q^{39} + 16 q^{43} + 72 q^{49} - 4 q^{51} - 8 q^{53} - 8 q^{57} - 24 q^{61} + 16 q^{63} - 16 q^{65} - 8 q^{67} + 32 q^{69} + 12 q^{71} - 4 q^{73} + 8 q^{75} + 16 q^{77} + 12 q^{79} - 48 q^{81} + 48 q^{83} + 8 q^{85} - 4 q^{89} + 8 q^{91} - 36 q^{97} + 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1520, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1520.2.q.a $2$ $12.137$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-1$$ $$-8$$ $$q+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-4q^{7}+\cdots$$
1520.2.q.b $2$ $12.137$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$1$$ $$0$$ $$q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$$
1520.2.q.c $2$ $12.137$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$1$$ $$8$$ $$q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}+\cdots$$
1520.2.q.d $2$ $12.137$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$4$$ $$q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+2q^{7}+\cdots$$
1520.2.q.e $2$ $12.137$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$-4$$ $$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-2q^{7}+\cdots$$
1520.2.q.f $2$ $12.137$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-2$$ $$q+(1-\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}-5q^{11}+\cdots$$
1520.2.q.g $2$ $12.137$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$1$$ $$8$$ $$q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}+\cdots$$
1520.2.q.h $4$ $12.137$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$0$$ $$-1$$ $$-2$$ $$-10$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-3-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$$
1520.2.q.i $6$ $12.137$ 6.0.1783323.2 None $$0$$ $$-1$$ $$3$$ $$-4$$ $$q+(-\beta _{3}+\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots$$
1520.2.q.j $6$ $12.137$ 6.0.3518667.1 None $$0$$ $$1$$ $$3$$ $$-4$$ $$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(-2+\cdots)q^{9}+\cdots$$
1520.2.q.k $8$ $12.137$ 8.0.4601315889.1 None $$0$$ $$-1$$ $$-4$$ $$-4$$ $$q+\beta _{7}q^{3}-\beta _{5}q^{5}+(\beta _{2}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$$
1520.2.q.l $8$ $12.137$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$4$$ $$4$$ $$q+(\beta _{1}+\beta _{4})q^{3}+\beta _{5}q^{5}+(1+\beta _{4}-2\beta _{7})q^{7}+\cdots$$
1520.2.q.m $8$ $12.137$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$1$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$$
1520.2.q.n $8$ $12.137$ 8.0.$$\cdots$$.1 None $$0$$ $$1$$ $$-4$$ $$6$$ $$q+\beta _{1}q^{3}-\beta _{4}q^{5}+(1-\beta _{3})q^{7}+(-4+\cdots)q^{9}+\cdots$$
1520.2.q.o $8$ $12.137$ 8.0.4601315889.1 None $$0$$ $$3$$ $$-4$$ $$8$$ $$q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{5}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$$
1520.2.q.p $10$ $12.137$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$-1$$ $$5$$ $$-10$$ $$q-\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(-1-\beta _{5})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1520, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1520, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(380, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(760, [\chi])$$$$^{\oplus 2}$$