Properties

Label 29.2.e
Level 29
Weight 2
Character orbit e
Rep. character \(\chi_{29}(4,\cdot)\)
Character field \(\Q(\zeta_{14})\)
Dimension 12
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 29.e (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 29 \)
Character field: \(\Q(\zeta_{14})\)
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 24 24 0
Cusp forms 12 12 0
Eisenstein series 12 12 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 14q^{8} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 14q^{8} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 7q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut 42q^{18} \) \(\mathstrut -\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 11q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 5q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 21q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut +\mathstrut 12q^{28} \) \(\mathstrut -\mathstrut 15q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 19q^{35} \) \(\mathstrut -\mathstrut 40q^{36} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 21q^{39} \) \(\mathstrut +\mathstrut 35q^{40} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 7q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 14q^{48} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 28q^{50} \) \(\mathstrut +\mathstrut 20q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 38q^{54} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 21q^{56} \) \(\mathstrut -\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 44q^{59} \) \(\mathstrut -\mathstrut 28q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut +\mathstrut 37q^{62} \) \(\mathstrut -\mathstrut 13q^{63} \) \(\mathstrut -\mathstrut 26q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 21q^{66} \) \(\mathstrut -\mathstrut 37q^{67} \) \(\mathstrut +\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 21q^{69} \) \(\mathstrut -\mathstrut 21q^{71} \) \(\mathstrut +\mathstrut 35q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 7q^{76} \) \(\mathstrut -\mathstrut 7q^{77} \) \(\mathstrut +\mathstrut 17q^{78} \) \(\mathstrut +\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut +\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 5q^{83} \) \(\mathstrut +\mathstrut 21q^{84} \) \(\mathstrut +\mathstrut 14q^{85} \) \(\mathstrut -\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 66q^{88} \) \(\mathstrut +\mathstrut 7q^{89} \) \(\mathstrut +\mathstrut 28q^{90} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 19q^{93} \) \(\mathstrut +\mathstrut 66q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 30q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 42q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.e.a \(12\) \(0.232\) 12.0.\(\cdots\).1 None \(-7\) \(-7\) \(-1\) \(-11\) \(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)