# Properties

 Label 1950.2.i Level $1950$ Weight $2$ Character orbit 1950.i Rep. character $\chi_{1950}(451,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $92$ Newform subspaces $35$ Sturm bound $840$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$35$$ Sturm bound: $$840$$ Trace bound: $$11$$ 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 888 92 796
Cusp forms 792 92 700
Eisenstein series 96 0 96

## Trace form

 $$92q - 2q^{2} - 46q^{4} + 4q^{8} - 46q^{9} + O(q^{10})$$ $$92q - 2q^{2} - 46q^{4} + 4q^{8} - 46q^{9} + 10q^{13} - 16q^{14} - 46q^{16} + 2q^{17} + 4q^{18} - 12q^{19} + 16q^{21} + 8q^{22} - 16q^{23} + 26q^{26} - 18q^{29} - 48q^{31} - 2q^{32} + 4q^{33} + 44q^{34} - 46q^{36} - 26q^{37} + 8q^{39} - 2q^{41} + 4q^{42} - 8q^{43} - 8q^{46} - 32q^{47} - 66q^{49} + 32q^{51} + 4q^{52} - 52q^{53} + 8q^{56} + 8q^{57} + 14q^{58} - 16q^{59} - 6q^{61} + 16q^{62} + 92q^{64} + 8q^{66} + 16q^{67} + 2q^{68} - 12q^{69} - 40q^{71} - 2q^{72} + 100q^{73} - 2q^{74} - 12q^{76} - 16q^{78} + 8q^{79} - 46q^{81} + 22q^{82} - 48q^{83} - 8q^{84} - 48q^{86} + 20q^{87} + 8q^{88} + 52q^{89} - 20q^{91} + 32q^{92} + 8q^{94} + 28q^{97} - 10q^{98} + O(q^{100})$$

## 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.i.a $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$-5$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.b $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.c $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.d $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.e $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.f $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$3$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.g $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.h $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.i $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-5$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.j $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-1$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.k $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-1$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.l $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.m $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.n $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$2$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.o $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$-3$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.p $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.q $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$1$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.r $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$1$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.s $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$2$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.t $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$0$$ $$-4$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.u $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$0$$ $$-4$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.v $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$0$$ $$0$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.w $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$0$$ $$2$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.x $$2$$ $$15.571$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$0$$ $$5$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
1950.2.i.y $$4$$ $$15.571$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$-2$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2})q^{3}+\cdots$$
1950.2.i.z $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$-2$$ $$-2$$ $$0$$ $$3$$ $$q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$$
1950.2.i.ba $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{10})$$ None $$-2$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$$
1950.2.i.bb $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{11})$$ None $$-2$$ $$2$$ $$0$$ $$2$$ $$q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$$
1950.2.i.bc $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{10})$$ None $$-2$$ $$2$$ $$0$$ $$4$$ $$q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$$
1950.2.i.bd $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{10})$$ None $$2$$ $$-2$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$$
1950.2.i.be $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{11})$$ None $$2$$ $$-2$$ $$0$$ $$-2$$ $$q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$$
1950.2.i.bf $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{10})$$ None $$2$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$$
1950.2.i.bg $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$2$$ $$2$$ $$0$$ $$-3$$ $$q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$$
1950.2.i.bh $$4$$ $$15.571$$ $$\Q(\zeta_{12})$$ None $$2$$ $$2$$ $$0$$ $$2$$ $$q+(1-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
1950.2.i.bi $$4$$ $$15.571$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$2$$ $$2$$ $$0$$ $$3$$ $$q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$$

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

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