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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 $1$

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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

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

Display 100 coefficients 10 coefficients

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

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