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Properties

Label 41.2.a
Level $41$
Weight $2$
Character orbit 41.a
Rep. character $\chi_{41}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 41.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(41))\).

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 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.

\(41\)Dim
\(-\)\(3\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 41
41.2.a.a 41.a 1.a $3$ $0.327$ 3.3.148.1 None \(-1\) \(0\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)