# Properties

 Label 41.2.a Level $41$ Weight $2$ Character orbit 41.a Rep. character $\chi_{41}(1,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $1$ Sturm bound $7$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 41.a (trivial) Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$7$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(41))$$.

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$41$$Dim.
$$-$$$$3$$

## Trace form

 $$3q - q^{2} + 5q^{4} - 2q^{5} - 6q^{6} + 6q^{7} - 9q^{8} - q^{9} + O(q^{10})$$ $$3q - q^{2} + 5q^{4} - 2q^{5} - 6q^{6} + 6q^{7} - 9q^{8} - q^{9} - 10q^{10} + 2q^{11} - 4q^{12} - 2q^{13} + 4q^{14} + 6q^{15} + 13q^{16} - 6q^{17} + 11q^{18} + 4q^{19} + 6q^{20} - 8q^{21} - 4q^{22} + 4q^{23} - 2q^{24} - 3q^{25} + 10q^{26} - 6q^{27} + 14q^{28} - 6q^{29} + 10q^{30} + 16q^{31} - 29q^{32} - 12q^{33} + 2q^{34} - 10q^{35} - 11q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 14q^{40} + 3q^{41} - 20q^{42} - 4q^{43} + 34q^{44} - 10q^{45} - 4q^{46} + 24q^{48} - q^{49} + 13q^{50} - 30q^{52} + 6q^{53} + 14q^{54} + 2q^{55} - 16q^{56} + 12q^{57} + 14q^{58} - 8q^{59} + 18q^{60} + 2q^{61} + 16q^{62} + 4q^{63} + 13q^{64} - 8q^{65} - 16q^{66} - 2q^{67} - 10q^{68} + 20q^{69} - 30q^{70} + 20q^{71} + 23q^{72} - 2q^{73} - 30q^{74} - 16q^{75} - 24q^{76} + 16q^{77} + 8q^{78} + 32q^{79} + 34q^{80} - 13q^{81} - q^{82} - 12q^{84} + 4q^{85} - 8q^{86} - 16q^{87} - 40q^{88} - 6q^{89} + 2q^{90} - 8q^{91} - 28q^{92} - 12q^{93} - 46q^{94} - 6q^{95} + 2q^{96} + 6q^{97} + 35q^{98} - 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(41))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 41
41.2.a.a $$3$$ $$0.327$$ 3.3.148.1 None $$-1$$ $$0$$ $$-2$$ $$6$$ $$-$$ $$q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$$