Properties

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

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Defining parameters

Level: \( N \) = \( 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 241.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
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.

\(241\)Dim.
\(+\)\(7\)
\(-\)\(12\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(241))\) into irreducible Hecke orbits

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