Properties

Label 29.2.a
Level 29
Weight 2
Character orbit 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 \(-2\) \(2\) \(-2\) \(0\) \(-\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4} \)
$3$ \( 1 - 2 T + 5 T^{2} - 6 T^{3} + 9 T^{4} \)
$5$ \( ( 1 + T + 5 T^{2} )^{2} \)
$7$ \( 1 + 6 T^{2} + 49 T^{4} \)
$11$ \( 1 - 2 T + 21 T^{2} - 22 T^{3} + 121 T^{4} \)
$13$ \( 1 + 2 T + 19 T^{2} + 26 T^{3} + 169 T^{4} \)
$17$ \( 1 + 4 T + 30 T^{2} + 68 T^{3} + 289 T^{4} \)
$19$ \( ( 1 - 6 T + 19 T^{2} )^{2} \)
$23$ \( 1 + 4 T + 18 T^{2} + 92 T^{3} + 529 T^{4} \)
$29$ \( ( 1 - T )^{2} \)
$31$ \( 1 - 6 T + 21 T^{2} - 186 T^{3} + 961 T^{4} \)
$37$ \( ( 1 + 4 T + 37 T^{2} )^{2} \)
$41$ \( 1 - 8 T + 26 T^{2} - 328 T^{3} + 1681 T^{4} \)
$43$ \( 1 - 10 T + 109 T^{2} - 430 T^{3} + 1849 T^{4} \)
$47$ \( 1 - 2 T + 77 T^{2} - 94 T^{3} + 2209 T^{4} \)
$53$ \( 1 - 2 T + 35 T^{2} - 106 T^{3} + 2809 T^{4} \)
$59$ \( 1 - 4 T + 90 T^{2} - 236 T^{3} + 3481 T^{4} \)
$61$ \( 1 + 4 T + 118 T^{2} + 244 T^{3} + 3721 T^{4} \)
$67$ \( 1 + 102 T^{2} + 4489 T^{4} \)
$71$ \( 1 + 12 T + 170 T^{2} + 852 T^{3} + 5041 T^{4} \)
$73$ \( ( 1 - 4 T + 73 T^{2} )^{2} \)
$79$ \( 1 + 2 T + 157 T^{2} + 158 T^{3} + 6241 T^{4} \)
$83$ \( 1 - 4 T + 138 T^{2} - 332 T^{3} + 6889 T^{4} \)
$89$ \( 1 + 8 T + 122 T^{2} + 712 T^{3} + 7921 T^{4} \)
$97$ \( 1 + 8 T + 138 T^{2} + 776 T^{3} + 9409 T^{4} \)
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