Properties

 Label 25.2.d Level $25$ Weight $2$ Character orbit 25.d Rep. character $\chi_{25}(6,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $4$ Newform subspaces $1$ Sturm bound $5$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 25.d (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$1$$ Sturm bound: $$5$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(25, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

 $$4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + O(q^{10})$$ $$4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} + 9 q^{13} + q^{14} - 5 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} - 5 q^{19} + 5 q^{20} - 2 q^{21} - 14 q^{22} - 11 q^{23} - 5 q^{25} - 12 q^{26} + 5 q^{27} + q^{28} + 5 q^{29} - 5 q^{30} + 3 q^{31} + 18 q^{32} + 8 q^{33} + 6 q^{34} + 5 q^{35} - 6 q^{36} - 7 q^{37} + 5 q^{38} + 9 q^{39} + 5 q^{40} + 8 q^{41} + q^{42} - 6 q^{43} + 6 q^{44} - 10 q^{45} + 13 q^{46} - 2 q^{47} - 6 q^{48} - 22 q^{49} - 10 q^{50} - 12 q^{51} - 12 q^{52} + 9 q^{53} - 15 q^{54} + 20 q^{55} - 10 q^{57} - 10 q^{58} + 13 q^{61} + 6 q^{62} - 6 q^{63} + 3 q^{64} + 6 q^{66} - 2 q^{67} - 4 q^{68} - q^{69} + 8 q^{71} + 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{75} + 20 q^{76} - 4 q^{77} + 3 q^{78} + 15 q^{79} - 15 q^{80} - q^{81} - 4 q^{82} + 9 q^{83} - 4 q^{84} - 20 q^{85} + 3 q^{86} - 10 q^{88} - 20 q^{89} - 12 q^{91} - 12 q^{92} - 12 q^{93} + q^{94} - 5 q^{95} - 2 q^{96} + 8 q^{97} + 11 q^{98} + 24 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(25, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.2.d.a $4$ $0.200$ $$\Q(\zeta_{10})$$ None $$-2$$ $$-1$$ $$-5$$ $$-2$$ $$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$$