# Properties

 Label 950.2.b Level $950$ Weight $2$ Character orbit 950.b Rep. character $\chi_{950}(799,\cdot)$ Character field $\Q$ Dimension $26$ Newform subspaces $8$ Sturm bound $300$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$300$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(950, [\chi])$$.

Total New Old
Modular forms 162 26 136
Cusp forms 138 26 112
Eisenstein series 24 0 24

## Trace form

 $$26 q - 26 q^{4} + 4 q^{6} - 38 q^{9} + O(q^{10})$$ $$26 q - 26 q^{4} + 4 q^{6} - 38 q^{9} + 8 q^{11} - 8 q^{14} + 26 q^{16} + 2 q^{19} + 32 q^{21} - 4 q^{24} - 24 q^{26} - 28 q^{29} + 4 q^{34} + 38 q^{36} - 8 q^{39} - 12 q^{41} - 8 q^{44} + 40 q^{46} - 62 q^{49} + 40 q^{51} - 16 q^{54} + 8 q^{56} - 24 q^{59} + 36 q^{61} - 26 q^{64} + 56 q^{69} + 8 q^{71} + 48 q^{74} - 2 q^{76} - 48 q^{79} + 42 q^{81} - 32 q^{84} + 52 q^{89} - 24 q^{91} - 56 q^{94} + 4 q^{96} + 32 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(950, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
950.2.b.a $2$ $7.586$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-5iq^{7}+\cdots$$
950.2.b.b $2$ $7.586$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots$$
950.2.b.c $2$ $7.586$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots$$
950.2.b.d $2$ $7.586$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots$$
950.2.b.e $2$ $7.586$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots$$
950.2.b.f $4$ $7.586$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots$$
950.2.b.g $6$ $7.586$ 6.0.4227136.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4})q^{3}-q^{4}+\cdots$$
950.2.b.h $6$ $7.586$ 6.0.63107136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(950, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(950, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 2}$$