# Properties

 Label 10.9.c Level 10 Weight 9 Character orbit c Rep. character $$\chi_{10}(3,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 8 Newforms 2 Sturm bound 13 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$10 = 2 \cdot 5$$ Weight: $$k$$ = $$9$$ Character orbit: $$[\chi]$$ = 10.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$5$$ Character field: $$\Q(i)$$ Newforms: $$2$$ Sturm bound: $$13$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(10, [\chi])$$.

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

## Trace form

 $$8q + 140q^{3} - 780q^{5} + 512q^{6} + 4540q^{7} + O(q^{10})$$ $$8q + 140q^{3} - 780q^{5} + 512q^{6} + 4540q^{7} - 6400q^{10} - 34584q^{11} + 17920q^{12} + 119280q^{13} - 252580q^{15} - 131072q^{16} + 202560q^{17} + 158720q^{18} + 53760q^{20} + 110696q^{21} + 40960q^{22} + 174540q^{23} - 368000q^{25} - 450048q^{26} - 704560q^{27} - 581120q^{28} + 1697280q^{30} + 2342456q^{31} - 3190840q^{33} + 4359900q^{35} - 618496q^{36} - 6531240q^{37} - 5076480q^{38} + 1146880q^{40} + 6454056q^{41} + 13150720q^{42} + 12059820q^{43} - 14797820q^{45} - 17410048q^{46} - 8748660q^{47} - 2293760q^{48} + 5414400q^{50} + 4713976q^{51} + 15267840q^{52} + 30279480q^{53} - 31155960q^{55} - 14155776q^{56} - 21729760q^{57} - 24194560q^{58} + 18675200q^{60} + 41805096q^{61} + 56017920q^{62} + 21701900q^{63} - 18428280q^{65} - 94667776q^{66} - 47676980q^{67} - 25927680q^{68} + 105582080q^{70} + 133410936q^{71} + 20316160q^{72} - 72484120q^{73} + 1104700q^{75} - 44615680q^{76} - 200406840q^{77} - 100792320q^{78} + 12779520q^{80} + 131272288q^{81} + 120186880q^{82} + 135315900q^{83} - 3822800q^{85} - 35731968q^{86} + 66654080q^{87} - 5242880q^{88} - 21256960q^{90} - 291657384q^{91} + 22341120q^{92} + 115691240q^{93} - 242319600q^{95} - 8388608q^{96} + 173745000q^{97} + 115169280q^{98} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(10, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
10.9.c.a $$4$$ $$4.074$$ $$\Q(i, \sqrt{249})$$ None $$-32$$ $$54$$ $$90$$ $$-1186$$ $$q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$$
10.9.c.b $$4$$ $$4.074$$ $$\Q(i, \sqrt{601})$$ None $$32$$ $$86$$ $$-870$$ $$5726$$ $$q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(10, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(10, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 2}$$