# Properties

 Label 950.2.h Level $950$ Weight $2$ Character orbit 950.h Rep. character $\chi_{950}(191,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $176$ Newform subspaces $5$ Sturm bound $300$ Trace bound $5$

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## Defining parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.h (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$5$$ Sturm bound: $$300$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 616 176 440
Cusp forms 584 176 408
Eisenstein series 32 0 32

## Trace form

 $$176q + 2q^{2} + 8q^{3} - 44q^{4} - 12q^{5} + 4q^{6} + 12q^{7} + 2q^{8} - 32q^{9} + O(q^{10})$$ $$176q + 2q^{2} + 8q^{3} - 44q^{4} - 12q^{5} + 4q^{6} + 12q^{7} + 2q^{8} - 32q^{9} + 10q^{10} - 2q^{11} - 12q^{12} + 12q^{13} + 12q^{15} - 44q^{16} - 2q^{17} - 40q^{18} + 2q^{19} - 2q^{20} + 8q^{22} + 2q^{23} - 16q^{24} - 36q^{25} - 36q^{26} - 4q^{27} - 8q^{28} + 12q^{29} + 12q^{30} + 12q^{31} - 8q^{32} - 44q^{33} - 30q^{34} + 38q^{35} - 32q^{36} + 30q^{37} + 40q^{39} + 10q^{40} - 24q^{41} + 12q^{42} + 20q^{43} + 8q^{44} + 60q^{45} + 36q^{47} - 12q^{48} + 172q^{49} + 10q^{50} + 24q^{51} + 12q^{52} + 18q^{53} + 16q^{54} + 56q^{55} + 60q^{58} - 12q^{59} - 28q^{60} + 36q^{61} - 72q^{62} - 2q^{63} - 44q^{64} + 54q^{65} + 16q^{66} - 4q^{67} + 8q^{68} - 136q^{69} - 112q^{70} + 40q^{71} + 10q^{72} - 8q^{73} - 52q^{74} - 20q^{75} - 8q^{76} + 56q^{77} - 60q^{78} - 16q^{79} + 8q^{80} - 24q^{81} - 92q^{82} - 50q^{83} - 36q^{85} + 24q^{86} + 56q^{87} - 12q^{88} - 38q^{89} + 10q^{90} - 16q^{91} - 8q^{92} + 64q^{93} + 2q^{95} + 4q^{96} + 120q^{97} + 18q^{98} + 52q^{99} + O(q^{100})$$

## 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.h.a $$4$$ $$7.586$$ $$\Q(\zeta_{10})$$ None $$1$$ $$4$$ $$5$$ $$-12$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots$$
950.2.h.b $$40$$ $$7.586$$ None $$-10$$ $$5$$ $$0$$ $$-12$$
950.2.h.c $$44$$ $$7.586$$ None $$-11$$ $$1$$ $$-1$$ $$18$$
950.2.h.d $$44$$ $$7.586$$ None $$11$$ $$-1$$ $$-11$$ $$-10$$
950.2.h.e $$44$$ $$7.586$$ None $$11$$ $$-1$$ $$-5$$ $$28$$

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

$$S_{2}^{\mathrm{old}}(950, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 2}$$