# Properties

 Label 241.2.a Level $241$ Weight $2$ Character orbit 241.a Rep. character $\chi_{241}(1,\cdot)$ Character field $\Q$ Dimension $19$ Newform subspaces $2$ Sturm bound $40$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$241$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 241.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$40$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(241))$$.

Total New Old
Modular forms 20 20 0
Cusp forms 19 19 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.

$$241$$Dim.
$$+$$$$7$$
$$-$$$$12$$

## Trace form

 $$19q - q^{2} - 2q^{3} + 15q^{4} - 2q^{5} - 6q^{6} - 4q^{7} + 3q^{8} + 13q^{9} + O(q^{10})$$ $$19q - q^{2} - 2q^{3} + 15q^{4} - 2q^{5} - 6q^{6} - 4q^{7} + 3q^{8} + 13q^{9} - 4q^{10} + 4q^{11} - 6q^{12} - 6q^{13} + 2q^{15} + 19q^{16} - 6q^{17} + 7q^{18} - 12q^{19} + 2q^{20} - 16q^{21} - 2q^{22} + 10q^{23} - 18q^{24} + 9q^{25} + 16q^{26} - 2q^{27} - 2q^{28} - 10q^{29} + 10q^{30} - 10q^{31} - 5q^{32} - 20q^{33} - 8q^{34} + 22q^{35} - 15q^{36} + 6q^{38} + 22q^{39} - 38q^{40} - 16q^{41} - 30q^{42} + 12q^{43} + 38q^{44} - 12q^{45} - 14q^{46} + 24q^{47} - 18q^{48} - 3q^{49} - 31q^{50} + 10q^{51} - 14q^{52} + 20q^{53} - 24q^{54} + 26q^{55} + 14q^{56} - 8q^{57} - 16q^{58} + 8q^{59} - 42q^{60} - 22q^{61} - 4q^{62} - 20q^{63} + 15q^{64} - 32q^{65} + 14q^{66} + 24q^{67} - 50q^{68} + 24q^{69} + 4q^{70} + 44q^{71} + 47q^{72} - 22q^{73} + 36q^{74} + 16q^{75} - 40q^{76} + 10q^{77} + 22q^{78} - 6q^{79} + 8q^{80} - 5q^{81} + 60q^{82} - 32q^{83} + 8q^{84} + 2q^{85} - 14q^{86} + 16q^{87} + 14q^{88} - 16q^{89} - 28q^{90} - 32q^{91} + 26q^{92} + 26q^{93} + 16q^{94} - 8q^{95} - 38q^{96} - 28q^{97} + 37q^{98} + 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(241))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 241
241.2.a.a $$7$$ $$1.924$$ 7.7.31056073.1 None $$-4$$ $$-3$$ $$-8$$ $$-7$$ $$+$$ $$q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
241.2.a.b $$12$$ $$1.924$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$3$$ $$1$$ $$6$$ $$3$$ $$-$$ $$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots$$