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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 29
29.2.a.a \(2\) \(0.232\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) \(-\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)