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Properties

Label 29.2.a
Level $29$
Weight $2$
Character orbit 29.a
Rep. character $\chi_{29}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(29))\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 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.

\(29\)Dim
\(-\)\(2\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 29
29.2.a.a 29.a 1.a $2$ $0.232$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)