Properties

 Label 950.2.e Level $950$ Weight $2$ Character orbit 950.e Rep. character $\chi_{950}(201,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $66$ Newform subspaces $15$ Sturm bound $300$ Trace bound $11$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$15$$ Sturm bound: $$300$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$11$$

Dimensions

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

Total New Old
Modular forms 324 66 258
Cusp forms 276 66 210
Eisenstein series 48 0 48

Trace form

 $$66 q - q^{2} - q^{3} - 33 q^{4} + q^{6} - 12 q^{7} + 2 q^{8} - 36 q^{9} + O(q^{10})$$ $$66 q - q^{2} - q^{3} - 33 q^{4} + q^{6} - 12 q^{7} + 2 q^{8} - 36 q^{9} - 2 q^{11} + 2 q^{12} + 10 q^{13} - 2 q^{14} - 33 q^{16} - 2 q^{17} - 12 q^{18} + 25 q^{19} + 26 q^{21} - q^{22} - 8 q^{23} + q^{24} - 12 q^{26} + 14 q^{27} + 6 q^{28} + 6 q^{29} - 16 q^{31} - q^{32} - 9 q^{33} + 2 q^{34} - 36 q^{36} + 8 q^{37} + 12 q^{38} - 52 q^{39} + 25 q^{41} + 14 q^{42} + 12 q^{43} + q^{44} - 24 q^{46} + 22 q^{47} - q^{48} + 42 q^{49} - 16 q^{51} + 10 q^{52} + 2 q^{53} - 29 q^{54} + 4 q^{56} - 16 q^{57} - 4 q^{58} + 35 q^{59} + 10 q^{61} + 8 q^{63} + 66 q^{64} - 9 q^{66} + 19 q^{67} + 4 q^{68} + 8 q^{69} + 2 q^{71} + 6 q^{72} + 27 q^{73} + 4 q^{74} - 17 q^{76} + 52 q^{77} + 2 q^{78} - 69 q^{81} - 9 q^{82} - 10 q^{83} - 52 q^{84} - 16 q^{86} - 28 q^{87} + 2 q^{88} + 34 q^{89} - 32 q^{91} - 8 q^{92} - 40 q^{93} - 52 q^{94} - 2 q^{96} - 27 q^{97} - 17 q^{98} - 36 q^{99} + O(q^{100})$$

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.e.a $2$ $7.586$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$-4$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
950.2.e.b $2$ $7.586$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$-4$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
950.2.e.c $2$ $7.586$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$8$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4q^{7}+q^{8}+\cdots$$
950.2.e.d $2$ $7.586$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$8$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
950.2.e.e $2$ $7.586$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$0$$ $$-8$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{7}-q^{8}+\cdots$$
950.2.e.f $2$ $7.586$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$0$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{7}-q^{8}+3\zeta_{6}q^{9}+\cdots$$
950.2.e.g $2$ $7.586$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$0$$ $$4$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
950.2.e.h $4$ $7.586$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$-2$$ $$-1$$ $$0$$ $$-10$$ $$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$$
950.2.e.i $4$ $7.586$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$-2$$ $$1$$ $$0$$ $$-4$$ $$q+(-1-\beta _{1})q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$$
950.2.e.j $4$ $7.586$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$2$$ $$-1$$ $$0$$ $$4$$ $$q+(1+\beta _{1})q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$$
950.2.e.k $4$ $7.586$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$2$$ $$0$$ $$0$$ $$-4$$ $$q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$$
950.2.e.l $8$ $7.586$ 8.0.$$\cdots$$.1 None $$-4$$ $$1$$ $$0$$ $$12$$ $$q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$$
950.2.e.m $8$ $7.586$ 8.0.$$\cdots$$.1 None $$4$$ $$-1$$ $$0$$ $$-12$$ $$q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$$
950.2.e.n $10$ $7.586$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$-5$$ $$0$$ $$0$$ $$-10$$ $$q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$$
950.2.e.o $10$ $7.586$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$5$$ $$0$$ $$0$$ $$10$$ $$q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(950, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 2}$$