Properties

Label 29.3.c
Level 29
Weight 3
Character orbit c
Rep. character \(\chi_{29}(12,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 8
Newforms 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 29.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 29 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(29, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

Trace form

\(8q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 54q^{12} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 32q^{16} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 20q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 108q^{20} \) \(\mathstrut -\mathstrut 36q^{21} \) \(\mathstrut +\mathstrut 168q^{24} \) \(\mathstrut +\mathstrut 104q^{25} \) \(\mathstrut -\mathstrut 54q^{26} \) \(\mathstrut -\mathstrut 98q^{27} \) \(\mathstrut +\mathstrut 128q^{29} \) \(\mathstrut -\mathstrut 220q^{30} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut -\mathstrut 106q^{32} \) \(\mathstrut -\mathstrut 252q^{36} \) \(\mathstrut -\mathstrut 84q^{37} \) \(\mathstrut -\mathstrut 90q^{39} \) \(\mathstrut +\mathstrut 226q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 190q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut +\mathstrut 292q^{45} \) \(\mathstrut +\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 354q^{48} \) \(\mathstrut -\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 144q^{52} \) \(\mathstrut +\mathstrut 252q^{53} \) \(\mathstrut +\mathstrut 400q^{54} \) \(\mathstrut -\mathstrut 74q^{55} \) \(\mathstrut -\mathstrut 192q^{56} \) \(\mathstrut +\mathstrut 326q^{58} \) \(\mathstrut -\mathstrut 40q^{59} \) \(\mathstrut -\mathstrut 258q^{60} \) \(\mathstrut -\mathstrut 208q^{61} \) \(\mathstrut +\mathstrut 36q^{65} \) \(\mathstrut -\mathstrut 414q^{66} \) \(\mathstrut -\mathstrut 296q^{68} \) \(\mathstrut +\mathstrut 120q^{69} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut -\mathstrut 636q^{72} \) \(\mathstrut -\mathstrut 188q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 12q^{75} \) \(\mathstrut +\mathstrut 592q^{76} \) \(\mathstrut +\mathstrut 180q^{77} \) \(\mathstrut +\mathstrut 600q^{78} \) \(\mathstrut -\mathstrut 382q^{79} \) \(\mathstrut -\mathstrut 124q^{81} \) \(\mathstrut +\mathstrut 228q^{82} \) \(\mathstrut +\mathstrut 280q^{83} \) \(\mathstrut -\mathstrut 124q^{84} \) \(\mathstrut +\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 34q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 64q^{89} \) \(\mathstrut +\mathstrut 128q^{90} \) \(\mathstrut -\mathstrut 460q^{94} \) \(\mathstrut -\mathstrut 380q^{95} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 66q^{98} \) \(\mathstrut +\mathstrut 552q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(29, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
29.3.c.a \(8\) \(0.790\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(2\) \(-2\) \(0\) \(-4\) \(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)