Properties

Label 29.2.b
Level 29
Weight 2
Character orbit b
Rep. character \(\chi_{29}(28,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(29, [\chi])\) into irreducible Hecke orbits

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 \(0\) \(0\) \(-6\) \(4\) \(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)