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Properties

Label 47.2.a
Level $47$
Weight $2$
Character orbit 47.a
Rep. character $\chi_{47}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 47.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(47))\).

Total New Old
Modular forms 5 5 0
Cusp forms 4 4 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.

\(47\)Dim
\(-\)\(4\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(47))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 47
47.2.a.a 47.a 1.a $4$ $0.375$ 4.4.1957.1 None \(1\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)