Properties

Label 29.2.d
Level 29
Weight 2
Character orbit d
Rep. character \(\chi_{29}(7,\cdot)\)
Character field \(\Q(\zeta_{7})\)
Dimension 6
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 29.d (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 29 \)
Character field: \(\Q(\zeta_{7})\)
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 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

Trace form

\(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 9q^{10} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 7q^{24} \) \(\mathstrut -\mathstrut 24q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 12q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 18q^{30} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 13q^{32} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut q^{35} \) \(\mathstrut +\mathstrut 5q^{36} \) \(\mathstrut +\mathstrut 11q^{37} \) \(\mathstrut +\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 3q^{39} \) \(\mathstrut +\mathstrut 14q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut +\mathstrut 20q^{44} \) \(\mathstrut +\mathstrut q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 6q^{48} \) \(\mathstrut -\mathstrut 22q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 10q^{52} \) \(\mathstrut +\mathstrut 3q^{53} \) \(\mathstrut +\mathstrut 6q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 7q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 16q^{58} \) \(\mathstrut -\mathstrut 56q^{59} \) \(\mathstrut -\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 3q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 5q^{66} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 12q^{68} \) \(\mathstrut -\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut +\mathstrut 21q^{71} \) \(\mathstrut -\mathstrut 25q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 48q^{75} \) \(\mathstrut -\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 11q^{77} \) \(\mathstrut +\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut -\mathstrut 18q^{80} \) \(\mathstrut +\mathstrut 18q^{81} \) \(\mathstrut -\mathstrut 2q^{82} \) \(\mathstrut +\mathstrut 17q^{83} \) \(\mathstrut +\mathstrut 3q^{84} \) \(\mathstrut -\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 16q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 42q^{88} \) \(\mathstrut +\mathstrut 7q^{89} \) \(\mathstrut +\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 5q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut -\mathstrut 32q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(6\) \(0.232\) \(\Q(\zeta_{14})\) None \(-2\) \(-5\) \(1\) \(1\) \(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)