# Properties

 Label 1950.2.z Level $1950$ Weight $2$ Character orbit 1950.z Rep. character $\chi_{1950}(1699,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $16$ Sturm bound $840$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.z (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$16$$ Sturm bound: $$840$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$

## Dimensions

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

Total New Old
Modular forms 888 80 808
Cusp forms 792 80 712
Eisenstein series 96 0 96

## Trace form

 $$80 q + 40 q^{4} + 40 q^{9} + O(q^{10})$$ $$80 q + 40 q^{4} + 40 q^{9} + 8 q^{11} + 16 q^{14} - 40 q^{16} - 20 q^{19} + 8 q^{21} + 28 q^{26} - 4 q^{29} - 32 q^{31} - 56 q^{34} - 40 q^{36} + 4 q^{39} - 52 q^{41} + 16 q^{44} - 8 q^{46} + 36 q^{49} + 16 q^{51} + 8 q^{56} + 72 q^{59} + 20 q^{61} - 80 q^{64} - 48 q^{66} + 8 q^{69} + 80 q^{71} + 20 q^{74} + 20 q^{76} + 40 q^{79} - 40 q^{81} + 4 q^{84} + 48 q^{86} - 80 q^{89} - 36 q^{91} - 32 q^{94} + 16 q^{99} + O(q^{100})$$

## 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.z.a $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.b $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.c $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.d $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.e $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.f $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.g $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.h $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.i $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.j $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.k $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.l $4$ $15.571$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
1950.2.z.m $8$ $15.571$ 8.0.1731891456.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{7})q^{2}+(-\beta _{3}-\beta _{7})q^{3}-\beta _{2}q^{4}+\cdots$$
1950.2.z.n $8$ $15.571$ 8.0.1731891456.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}-\beta _{7})q^{2}+(\beta _{3}+\beta _{7})q^{3}-\beta _{2}q^{4}+\cdots$$
1950.2.z.o $8$ $15.571$ 8.0.3317760000.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots$$
1950.2.z.p $8$ $15.571$ 8.0.3317760000.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+\beta _{2}q^{6}+\cdots$$

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

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