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

Downloads

Learn more about

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 \(3\) \(1\) \(6\) \(3\) \(-\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)