Properties

 Label 95.2.k Level $95$ Weight $2$ Character orbit 95.k Rep. character $\chi_{95}(6,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $36$ Newform subspaces $2$ Sturm bound $20$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 95.k (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$2$$ Sturm bound: $$20$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(95, [\chi])$$.

Total New Old
Modular forms 72 36 36
Cusp forms 48 36 12
Eisenstein series 24 0 24

Trace form

 $$36 q - 6 q^{3} - 6 q^{4} - 12 q^{6} - 18 q^{8} - 18 q^{9} + O(q^{10})$$ $$36 q - 6 q^{3} - 6 q^{4} - 12 q^{6} - 18 q^{8} - 18 q^{9} - 6 q^{10} - 12 q^{12} - 6 q^{13} + 12 q^{14} + 18 q^{16} + 36 q^{18} - 12 q^{19} - 18 q^{21} + 24 q^{22} + 12 q^{23} + 6 q^{24} - 18 q^{26} - 18 q^{27} - 36 q^{28} + 6 q^{29} - 24 q^{30} + 12 q^{31} + 60 q^{32} - 36 q^{33} + 12 q^{34} - 6 q^{35} + 54 q^{36} - 24 q^{37} - 48 q^{38} + 48 q^{39} - 12 q^{40} - 36 q^{41} + 30 q^{42} - 42 q^{43} + 12 q^{44} + 30 q^{46} + 54 q^{47} - 30 q^{48} + 6 q^{49} - 6 q^{50} - 18 q^{51} - 30 q^{52} + 12 q^{53} - 36 q^{54} - 72 q^{56} + 42 q^{57} + 48 q^{58} + 36 q^{59} + 12 q^{60} - 24 q^{61} - 12 q^{62} + 78 q^{63} + 12 q^{64} - 6 q^{65} + 6 q^{66} - 24 q^{67} + 48 q^{68} + 42 q^{69} + 72 q^{70} + 12 q^{71} - 48 q^{72} + 30 q^{73} - 54 q^{74} + 12 q^{75} - 6 q^{76} - 36 q^{77} + 24 q^{78} - 42 q^{79} + 48 q^{80} + 42 q^{81} - 72 q^{82} + 36 q^{84} + 48 q^{85} + 30 q^{86} - 60 q^{87} + 12 q^{88} - 60 q^{89} - 30 q^{90} + 24 q^{91} - 108 q^{92} - 36 q^{94} - 84 q^{96} - 60 q^{97} + 36 q^{98} - 90 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(95, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.2.k.a $18$ $0.759$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$-3$$ $$-3$$ $$0$$ $$0$$ $$q+(-\beta _{4}+\beta _{15})q^{2}+(\beta _{5}+\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots$$
95.2.k.b $18$ $0.759$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$3$$ $$-3$$ $$0$$ $$0$$ $$q-\beta _{14}q^{2}+(-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{15}+\cdots)q^{3}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(95, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(95, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 2}$$