Properties

 Label 950.2.r Level $950$ Weight $2$ Character orbit 950.r Rep. character $\chi_{950}(11,\cdot)$ Character field $\Q(\zeta_{15})$ Dimension $400$ Newform subspaces $2$ Sturm bound $300$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.r (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$475$$ Character field: $$\Q(\zeta_{15})$$ Newform subspaces: $$2$$ Sturm bound: $$300$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

Dimensions

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

Total New Old
Modular forms 1232 400 832
Cusp forms 1168 400 768
Eisenstein series 64 0 64

Trace form

 $$400q + 50q^{4} + 2q^{5} - 8q^{7} + 50q^{9} + O(q^{10})$$ $$400q + 50q^{4} + 2q^{5} - 8q^{7} + 50q^{9} + 12q^{11} + 16q^{13} + 8q^{14} + 6q^{15} + 50q^{16} - 18q^{17} - 32q^{18} - 12q^{19} - 4q^{20} + 32q^{21} + 12q^{22} - 2q^{23} + 10q^{25} - 36q^{27} + 4q^{28} + 24q^{29} - 12q^{30} + 8q^{34} - 20q^{35} + 50q^{36} + 16q^{37} + 20q^{38} - 24q^{39} + 16q^{41} + 32q^{42} + 60q^{43} + 4q^{44} + 8q^{45} + 32q^{46} - 44q^{47} + 360q^{49} - 8q^{50} - 52q^{51} + 16q^{52} - 36q^{53} - 12q^{54} - 16q^{56} + 108q^{57} + 48q^{59} - 14q^{60} + 28q^{61} - 8q^{62} - 66q^{63} - 100q^{64} + 216q^{65} - 16q^{66} - 72q^{67} - 104q^{68} - 16q^{69} - 16q^{70} + 14q^{71} + 16q^{72} - 40q^{73} - 80q^{75} + 8q^{76} - 128q^{77} - 60q^{78} - 8q^{79} + 2q^{80} - 6q^{81} - 8q^{82} - 56q^{83} + 56q^{84} - 10q^{85} + 20q^{86} - 176q^{87} + 16q^{88} + 12q^{89} - 114q^{90} + 8q^{91} + 8q^{92} - 132q^{93} - 32q^{95} + 2q^{97} + 16q^{98} - 12q^{99} + O(q^{100})$$

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.r.a $$200$$ $$7.586$$ None $$-25$$ $$0$$ $$1$$ $$-36$$
950.2.r.b $$200$$ $$7.586$$ None $$25$$ $$0$$ $$1$$ $$28$$

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

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