# Properties

 Label 1950.2.b Level $1950$ Weight $2$ Character orbit 1950.b Rep. character $\chi_{1950}(1351,\cdot)$ Character field $\Q$ Dimension $42$ Newform subspaces $13$ 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.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$13$$ Sturm bound: $$840$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$, $$19$$

## Dimensions

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

Total New Old
Modular forms 444 42 402
Cusp forms 396 42 354
Eisenstein series 48 0 48

## Trace form

 $$42q + 2q^{3} - 42q^{4} + 42q^{9} + O(q^{10})$$ $$42q + 2q^{3} - 42q^{4} + 42q^{9} - 2q^{12} + 2q^{13} - 12q^{14} + 42q^{16} - 4q^{17} - 8q^{23} + 8q^{26} + 2q^{27} - 28q^{29} - 42q^{36} + 12q^{38} - 18q^{39} + 4q^{42} - 24q^{43} + 2q^{48} - 58q^{49} - 12q^{51} - 2q^{52} + 20q^{53} + 12q^{56} + 60q^{61} + 28q^{62} - 42q^{64} + 4q^{68} - 8q^{69} + 56q^{74} + 64q^{77} - 12q^{78} + 24q^{79} + 42q^{81} + 12q^{82} + 12q^{87} - 24q^{91} + 8q^{92} - 40q^{94} + O(q^{100})$$

## 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.b.a $$2$$ $$15.571$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{6}+2iq^{7}+\cdots$$
1950.2.b.b $$2$$ $$15.571$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}-q^{4}-iq^{6}+3iq^{7}+\cdots$$
1950.2.b.c $$2$$ $$15.571$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{6}+2iq^{7}+\cdots$$
1950.2.b.d $$2$$ $$15.571$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}+iq^{6}+3iq^{7}+\cdots$$
1950.2.b.e $$2$$ $$15.571$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-iq^{2}+q^{3}-q^{4}-iq^{6}+iq^{8}+q^{9}+\cdots$$
1950.2.b.f $$2$$ $$15.571$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-iq^{2}+q^{3}-q^{4}-iq^{6}+2iq^{7}+\cdots$$
1950.2.b.g $$2$$ $$15.571$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{8}+q^{9}+\cdots$$
1950.2.b.h $$4$$ $$15.571$$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1950.2.b.i $$4$$ $$15.571$$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$$
1950.2.b.j $$4$$ $$15.571$$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$$
1950.2.b.k $$4$$ $$15.571$$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1950.2.b.l $$6$$ $$15.571$$ 6.0.350464.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-q^{3}-q^{4}-\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$$
1950.2.b.m $$6$$ $$15.571$$ 6.0.350464.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+q^{3}-q^{4}+\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1950, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(325, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(650, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(975, [\chi])$$$$^{\oplus 2}$$