# Properties

 Label 825.2.r Level $825$ Weight $2$ Character orbit 825.r Rep. character $\chi_{825}(31,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $240$ Newform subspaces $3$ Sturm bound $240$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 825.r (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$275$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$3$$ Sturm bound: $$240$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(825, [\chi])$$.

Total New Old
Modular forms 496 240 256
Cusp forms 464 240 224
Eisenstein series 32 0 32

## Trace form

 $$240q + 240q^{4} - 4q^{5} - 4q^{6} + 4q^{7} - 60q^{9} + O(q^{10})$$ $$240q + 240q^{4} - 4q^{5} - 4q^{6} + 4q^{7} - 60q^{9} - 2q^{10} - 4q^{11} + 4q^{12} + 12q^{13} - 8q^{15} + 264q^{16} + 2q^{17} + 56q^{19} - 36q^{20} - 8q^{21} - 30q^{22} - 32q^{23} - 12q^{24} + 12q^{25} + 10q^{26} + 14q^{28} - 16q^{30} + 2q^{31} + 60q^{32} - 16q^{33} - 2q^{35} - 60q^{36} + 10q^{37} - 56q^{38} - 16q^{39} - 54q^{40} - 24q^{41} + 2q^{42} - 48q^{43} - 44q^{44} + 6q^{45} - 12q^{46} + 26q^{47} + 8q^{48} - 52q^{49} + 6q^{50} - 16q^{51} + 32q^{52} - 24q^{53} - 4q^{54} - 16q^{55} - 12q^{57} - 88q^{58} - 24q^{59} - 40q^{60} - 18q^{61} - 10q^{62} + 4q^{63} + 264q^{64} - 34q^{65} - 8q^{66} + 44q^{67} - 26q^{68} - 8q^{69} + 36q^{70} - 24q^{71} - 26q^{73} + 22q^{74} + 28q^{75} + 188q^{76} - 86q^{77} - 24q^{78} - 38q^{79} + 8q^{80} - 60q^{81} + 76q^{82} + 164q^{83} - 24q^{84} + 46q^{85} - 88q^{86} - 40q^{87} - 114q^{88} + 8q^{90} - 10q^{91} - 110q^{92} + 72q^{93} - 84q^{94} + 60q^{95} - 28q^{96} + 70q^{97} - 184q^{98} + 6q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(825, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
825.2.r.a $$4$$ $$6.588$$ $$\Q(\zeta_{10})$$ None $$0$$ $$-1$$ $$5$$ $$1$$ $$q+(-1-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots$$
825.2.r.b $$116$$ $$6.588$$ None $$8$$ $$-29$$ $$-1$$ $$-3$$
825.2.r.c $$120$$ $$6.588$$ None $$-8$$ $$30$$ $$-8$$ $$6$$

## Decomposition of $$S_{2}^{\mathrm{old}}(825, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(825, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 2}$$