# Properties

 Label 1950.2.y Level $1950$ Weight $2$ Character orbit 1950.y Rep. character $\chi_{1950}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $88$ Newform subspaces $14$ Sturm bound $840$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.y (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$14$$ Sturm bound: $$840$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1950, [\chi])$$.

Total New Old
Modular forms 888 88 800
Cusp forms 792 88 704
Eisenstein series 96 0 96

## Trace form

 $$88 q - 44 q^{4} + 44 q^{9} + O(q^{10})$$ $$88 q - 44 q^{4} + 44 q^{9} - 24 q^{11} - 16 q^{14} - 44 q^{16} - 36 q^{19} - 24 q^{26} - 8 q^{29} + 44 q^{36} - 12 q^{39} + 96 q^{41} + 24 q^{46} - 64 q^{49} - 48 q^{51} + 8 q^{56} + 72 q^{59} - 24 q^{61} + 88 q^{64} + 16 q^{66} - 40 q^{69} + 48 q^{71} + 36 q^{76} - 8 q^{79} - 44 q^{81} + 12 q^{84} - 72 q^{89} + 12 q^{91} + 16 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1950, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1950.2.y.a $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$-6$$ $$q+(-1+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
1950.2.y.b $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
1950.2.y.c $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1950.2.y.d $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$6$$ $$q-\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1950.2.y.e $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$-6$$ $$q+(1-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
1950.2.y.f $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$-4$$ $$q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1950.2.y.g $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$2$$ $$q+(1-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
1950.2.y.h $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$6$$ $$q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1950.2.y.i $8$ $15.571$ $$\Q(\zeta_{24})$$ None $$-4$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+\zeta_{24}^{4})q^{2}-\zeta_{24}^{2}q^{3}-\zeta_{24}^{4}q^{4}+\cdots$$
1950.2.y.j $8$ $15.571$ 8.0.$$\cdots$$.1 None $$-4$$ $$0$$ $$0$$ $$2$$ $$q+(-1+\beta _{6})q^{2}+(\beta _{2}+\beta _{5})q^{3}-\beta _{6}q^{4}+\cdots$$
1950.2.y.k $8$ $15.571$ 8.0.$$\cdots$$.1 None $$4$$ $$0$$ $$0$$ $$-2$$ $$q+(1-\beta _{6})q^{2}+(-\beta _{2}-\beta _{5})q^{3}-\beta _{6}q^{4}+\cdots$$
1950.2.y.l $8$ $15.571$ $$\Q(\zeta_{24})$$ None $$4$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{24}^{4}q^{2}+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1950.2.y.m $12$ $15.571$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$0$$ $$0$$ $$4$$ $$q+(-1+\beta _{4})q^{2}-\beta _{9}q^{3}-\beta _{4}q^{4}+\beta _{8}q^{6}+\cdots$$
1950.2.y.n $12$ $15.571$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$6$$ $$0$$ $$0$$ $$-4$$ $$q+(1-\beta _{4})q^{2}+\beta _{9}q^{3}-\beta _{4}q^{4}+\beta _{8}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1950, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1950, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(325, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(650, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(975, [\chi])$$$$^{\oplus 2}$$