Properties

Label 241.2.l
Level $241$
Weight $2$
Character orbit 241.l
Rep. character $\chi_{241}(6,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $144$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 241.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(241, [\chi])\).

Total New Old
Modular forms 160 160 0
Cusp forms 144 144 0
Eisenstein series 16 16 0

Trace form

\( 144q - 10q^{3} - 120q^{4} - 10q^{5} + 6q^{6} - 10q^{7} + 14q^{9} + O(q^{10}) \) \( 144q - 10q^{3} - 120q^{4} - 10q^{5} + 6q^{6} - 10q^{7} + 14q^{9} - 2q^{10} - 14q^{11} - 20q^{12} - 26q^{13} + 6q^{14} - 60q^{15} + 56q^{16} - 38q^{17} + 10q^{18} + 12q^{19} - 30q^{20} - 16q^{21} - 4q^{23} + 10q^{25} + 16q^{26} - 10q^{27} - 4q^{28} - 10q^{29} - 44q^{31} + 20q^{33} + 136q^{34} - 14q^{35} + 30q^{36} - 12q^{37} + 22q^{38} + 64q^{40} - 10q^{41} + 26q^{42} + 6q^{43} + 8q^{44} - 40q^{45} - 56q^{46} - 10q^{47} - 10q^{49} - 170q^{50} + 26q^{51} + 2q^{52} + 50q^{53} + 32q^{55} + 42q^{56} + 78q^{57} + 38q^{58} + 10q^{59} - 72q^{60} + 50q^{61} - 44q^{62} + 150q^{63} + 104q^{64} + 58q^{65} - 30q^{66} + 20q^{67} + 52q^{68} - 42q^{69} + 58q^{70} - 26q^{71} + 100q^{72} - 32q^{73} - 98q^{74} - 140q^{75} - 128q^{76} - 130q^{77} - 130q^{78} + 50q^{79} - 80q^{80} + 60q^{81} - 26q^{82} + 2q^{83} - 98q^{84} + 6q^{85} - 8q^{86} + 62q^{87} + 52q^{88} + 84q^{89} - 24q^{90} + 22q^{91} + 10q^{92} + 20q^{93} + 130q^{94} - 104q^{95} + 76q^{96} + 52q^{97} + 10q^{98} - 74q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(241, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
241.2.l.a \(144\) \(1.924\) None \(0\) \(-10\) \(-10\) \(-10\)