Properties

Label 29.2.b
Level 29
Weight 2
Character orbit b
Rep. character \(\chi_{29}(28,\cdot)\)
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(29, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\( 2q - 6q^{4} - 6q^{5} + 10q^{6} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 2q - 6q^{4} - 6q^{5} + 10q^{6} + 4q^{7} - 4q^{9} - 2q^{13} - 2q^{16} + 18q^{20} - 10q^{22} + 12q^{23} - 10q^{24} + 8q^{25} - 12q^{28} - 6q^{29} - 30q^{30} + 10q^{33} + 20q^{34} - 12q^{35} + 12q^{36} + 20q^{42} + 12q^{45} - 6q^{49} - 20q^{51} + 6q^{52} - 18q^{53} + 10q^{54} - 20q^{58} + 12q^{59} - 30q^{62} - 8q^{63} + 26q^{64} + 6q^{65} + 16q^{67} - 10q^{78} + 6q^{80} - 22q^{81} + 20q^{82} - 12q^{83} + 30q^{86} + 20q^{87} + 10q^{88} - 4q^{91} - 36q^{92} + 30q^{93} - 10q^{94} - 30q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(29, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
29.2.b.a \(2\) \(0.232\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-6\) \(4\) \(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T^{2} + 4 T^{4} \)
$3$ \( 1 - T^{2} + 9 T^{4} \)
$5$ \( ( 1 + 3 T + 5 T^{2} )^{2} \)
$7$ \( ( 1 - 2 T + 7 T^{2} )^{2} \)
$11$ \( 1 - 17 T^{2} + 121 T^{4} \)
$13$ \( ( 1 + T + 13 T^{2} )^{2} \)
$17$ \( 1 - 14 T^{2} + 289 T^{4} \)
$19$ \( ( 1 - 19 T^{2} )^{2} \)
$23$ \( ( 1 - 6 T + 23 T^{2} )^{2} \)
$29$ \( 1 + 6 T + 29 T^{2} \)
$31$ \( 1 - 17 T^{2} + 961 T^{4} \)
$37$ \( ( 1 - 37 T^{2} )^{2} \)
$41$ \( ( 1 - 12 T + 41 T^{2} )( 1 + 12 T + 41 T^{2} ) \)
$43$ \( 1 - 41 T^{2} + 1849 T^{4} \)
$47$ \( 1 - 89 T^{2} + 2209 T^{4} \)
$53$ \( ( 1 + 9 T + 53 T^{2} )^{2} \)
$59$ \( ( 1 - 6 T + 59 T^{2} )^{2} \)
$61$ \( ( 1 - 8 T + 61 T^{2} )( 1 + 8 T + 61 T^{2} ) \)
$67$ \( ( 1 - 8 T + 67 T^{2} )^{2} \)
$71$ \( ( 1 + 71 T^{2} )^{2} \)
$73$ \( ( 1 - 73 T^{2} )^{2} \)
$79$ \( 1 - 113 T^{2} + 6241 T^{4} \)
$83$ \( ( 1 + 6 T + 83 T^{2} )^{2} \)
$89$ \( 1 - 158 T^{2} + 7921 T^{4} \)
$97$ \( 1 - 14 T^{2} + 9409 T^{4} \)
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