Properties

 Label 50.3.c Level $50$ Weight $3$ Character orbit 50.c Rep. character $\chi_{50}(7,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $6$ Newform subspaces $3$ Sturm bound $22$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$50 = 2 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 50.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$22$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(50, [\chi])$$.

Total New Old
Modular forms 42 6 36
Cusp forms 18 6 12
Eisenstein series 24 0 24

Trace form

 $$6 q + 2 q^{2} + 4 q^{3} - 16 q^{6} - 4 q^{7} - 4 q^{8} + O(q^{10})$$ $$6 q + 2 q^{2} + 4 q^{3} - 16 q^{6} - 4 q^{7} - 4 q^{8} + 32 q^{11} + 8 q^{12} - 6 q^{13} - 24 q^{16} - 14 q^{17} - 2 q^{18} - 88 q^{21} - 16 q^{22} + 4 q^{23} + 84 q^{26} + 40 q^{27} + 8 q^{28} + 72 q^{31} - 8 q^{32} - 32 q^{33} + 68 q^{36} + 6 q^{37} + 40 q^{38} - 208 q^{41} - 16 q^{42} + 84 q^{43} - 16 q^{46} + 36 q^{47} - 16 q^{48} + 232 q^{51} - 12 q^{52} - 106 q^{53} - 32 q^{56} - 80 q^{57} - 80 q^{58} + 32 q^{61} + 104 q^{62} + 4 q^{63} - 352 q^{66} - 124 q^{67} + 28 q^{68} - 248 q^{71} - 4 q^{72} + 94 q^{73} - 80 q^{76} + 32 q^{77} - 24 q^{78} + 466 q^{81} - 16 q^{82} - 36 q^{83} + 384 q^{86} + 160 q^{87} + 32 q^{88} + 312 q^{91} + 8 q^{92} + 208 q^{93} + 64 q^{96} + 126 q^{97} + 82 q^{98} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(50, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
50.3.c.a $2$ $1.362$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$6$$ $$0$$ $$-6$$ $$q+(-1-i)q^{2}+(3-3i)q^{3}+2iq^{4}+\cdots$$
50.3.c.b $2$ $1.362$ $$\Q(\sqrt{-1})$$ None $$2$$ $$-6$$ $$0$$ $$6$$ $$q+(1+i)q^{2}+(-3+3i)q^{3}+2iq^{4}+\cdots$$
50.3.c.c $2$ $1.362$ $$\Q(\sqrt{-1})$$ None $$2$$ $$4$$ $$0$$ $$-4$$ $$q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(50, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(50, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 2}$$