# Properties

 Label 41.2.c Level $41$ Weight $2$ Character orbit 41.c Rep. character $\chi_{41}(9,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $6$ Newform subspaces $1$ Sturm bound $7$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 41.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$41$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$7$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(41, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

## Trace form

 $$6q - 4q^{3} - 10q^{4} + 2q^{6} - 2q^{7} + O(q^{10})$$ $$6q - 4q^{3} - 10q^{4} + 2q^{6} - 2q^{7} + 24q^{10} + 6q^{11} - 12q^{12} - 10q^{13} - 4q^{14} + 2q^{15} + 10q^{16} - 18q^{17} + 10q^{18} + 4q^{19} - 16q^{22} - 12q^{23} - 18q^{24} - 2q^{25} + 18q^{26} + 26q^{27} + 22q^{28} + 10q^{29} + 6q^{30} - 8q^{31} + 6q^{34} + 6q^{35} - 26q^{38} - 36q^{40} + 14q^{41} - 20q^{42} - 22q^{44} - 16q^{45} + 12q^{47} + 24q^{51} + 10q^{52} + 6q^{53} - 38q^{54} + 10q^{55} + 24q^{56} + 20q^{57} + 10q^{58} + 4q^{59} + 34q^{60} - 32q^{63} + 30q^{64} - 8q^{65} + 16q^{66} - 18q^{67} + 30q^{68} + 8q^{69} - 30q^{70} - 24q^{71} + 54q^{72} - 24q^{75} - 32q^{76} - 8q^{79} - 78q^{81} + 20q^{82} - 20q^{83} - 24q^{85} - 44q^{86} + 42q^{89} + 20q^{92} + 36q^{93} - 22q^{94} + 30q^{95} - 26q^{96} + 2q^{97} + 14q^{98} + 36q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(41, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
41.2.c.a $$6$$ $$0.327$$ 6.0.5089536.1 None $$0$$ $$-4$$ $$0$$ $$-2$$ $$q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots$$