# Properties

 Label 1950.2.e Level $1950$ Weight $2$ Character orbit 1950.e Rep. character $\chi_{1950}(1249,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $16$ Sturm bound $840$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$16$$ Sturm bound: $$840$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$, $$31$$

## Dimensions

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

Total New Old
Modular forms 444 36 408
Cusp forms 396 36 360
Eisenstein series 48 0 48

## Trace form

 $$36 q - 36 q^{4} + 4 q^{6} - 36 q^{9} + O(q^{10})$$ $$36 q - 36 q^{4} + 4 q^{6} - 36 q^{9} + 16 q^{11} + 36 q^{16} - 8 q^{19} + 8 q^{21} - 4 q^{24} + 16 q^{29} - 24 q^{31} - 16 q^{34} + 36 q^{36} - 32 q^{41} - 16 q^{44} + 32 q^{46} - 12 q^{49} - 16 q^{51} - 4 q^{54} + 32 q^{61} - 36 q^{64} + 16 q^{69} - 32 q^{71} + 32 q^{74} + 8 q^{76} - 8 q^{79} + 36 q^{81} - 8 q^{84} - 64 q^{86} - 16 q^{89} - 8 q^{91} + 32 q^{94} + 4 q^{96} - 16 q^{99} + O(q^{100})$$

## 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.e.a $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots$$
1950.2.e.b $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots$$
1950.2.e.c $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$$
1950.2.e.d $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$$
1950.2.e.e $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$$
1950.2.e.f $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$$
1950.2.e.g $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots$$
1950.2.e.h $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots$$
1950.2.e.i $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots$$
1950.2.e.j $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots$$
1950.2.e.k $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$$
1950.2.e.l $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots$$
1950.2.e.m $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots$$
1950.2.e.n $2$ $15.571$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots$$
1950.2.e.o $4$ $15.571$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}-q^{4}+q^{6}+\zeta_{8}^{2}q^{7}+\cdots$$
1950.2.e.p $4$ $15.571$ $$\Q(i, \sqrt{41})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1950, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(325, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(650, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(975, [\chi])$$$$^{\oplus 2}$$