# Properties

 Label 1950.2.bc Level $1950$ Weight $2$ Character orbit 1950.bc Rep. character $\chi_{1950}(751,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $88$ Newform subspaces $11$ 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.bc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$11$$ Sturm bound: $$840$$ Trace bound: $$11$$ 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

 $$88q + 44q^{4} - 44q^{9} + O(q^{10})$$ $$88q + 44q^{4} - 44q^{9} - 24q^{11} + 12q^{13} - 44q^{16} - 8q^{17} + 36q^{19} + 8q^{23} - 20q^{26} - 20q^{29} - 12q^{33} + 44q^{36} - 12q^{37} + 16q^{39} + 12q^{41} - 4q^{42} + 8q^{43} + 24q^{46} + 32q^{49} + 16q^{53} + 36q^{58} + 24q^{59} + 16q^{61} + 8q^{62} - 88q^{64} - 24q^{66} + 24q^{67} + 8q^{68} - 4q^{69} + 72q^{71} + 28q^{74} + 36q^{76} + 32q^{77} + 40q^{79} - 44q^{81} + 12q^{82} - 24q^{84} + 12q^{87} + 48q^{89} - 36q^{91} + 16q^{92} - 24q^{93} + 16q^{94} - 72q^{98} + O(q^{100})$$

## 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.bc.a $$4$$ $$15.571$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1950.2.bc.b $$4$$ $$15.571$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1950.2.bc.c $$4$$ $$15.571$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$6$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots$$
1950.2.bc.d $$4$$ $$15.571$$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$-6$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots$$
1950.2.bc.e $$8$$ $$15.571$$ $$\Q(\zeta_{24})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}-\zeta_{24}^{4}q^{3}+(1+\cdots)q^{4}+\cdots$$
1950.2.bc.f $$8$$ $$15.571$$ $$\Q(\zeta_{24})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\zeta_{24}^{2}q^{2}+(1-\zeta_{24}^{4})q^{3}+\zeta_{24}^{4}q^{4}+\cdots$$
1950.2.bc.g $$8$$ $$15.571$$ 8.0.$$\cdots$$.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{5})q^{2}+(1-\beta _{6})q^{3}+\beta _{6}q^{4}+\cdots$$
1950.2.bc.h $$12$$ $$15.571$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$-6$$ $$q-\beta _{8}q^{2}-\beta _{4}q^{3}+(1-\beta _{4})q^{4}+\beta _{9}q^{6}+\cdots$$
1950.2.bc.i $$12$$ $$15.571$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$12$$ $$q+(\beta _{4}+\beta _{7})q^{2}+\beta _{6}q^{3}+(1+\beta _{6})q^{4}+\cdots$$
1950.2.bc.j $$12$$ $$15.571$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$6$$ $$0$$ $$-12$$ $$q+(-\beta _{4}-\beta _{7})q^{2}-\beta _{6}q^{3}+(1+\beta _{6}+\cdots)q^{4}+\cdots$$
1950.2.bc.k $$12$$ $$15.571$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$6$$ $$0$$ $$6$$ $$q+\beta _{8}q^{2}+\beta _{4}q^{3}+(1-\beta _{4})q^{4}+\beta _{9}q^{6}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1950, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(325, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(650, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(975, [\chi])$$$$^{\oplus 2}$$