Properties

Label 69.3.b
Level $69$
Weight $3$
Character orbit 69.b
Rep. character $\chi_{69}(47,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 69.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(69, [\chi])\).

Total New Old
Modular forms 18 14 4
Cusp forms 14 14 0
Eisenstein series 4 0 4

Trace form

\( 14q - 4q^{3} - 24q^{4} + 11q^{6} - 4q^{7} - 8q^{9} + O(q^{10}) \) \( 14q - 4q^{3} - 24q^{4} + 11q^{6} - 4q^{7} - 8q^{9} - 8q^{10} + 19q^{12} - 14q^{15} + 72q^{16} - 31q^{18} + 8q^{19} - 2q^{21} - 84q^{22} - 44q^{24} + 38q^{25} + 62q^{27} + 76q^{28} + 62q^{30} - 144q^{31} + 90q^{33} - 68q^{34} + 3q^{36} + 48q^{37} - 78q^{39} + 120q^{40} - 76q^{42} - 48q^{43} - 18q^{45} - 317q^{48} - 30q^{49} + 18q^{51} - 6q^{52} + 312q^{54} + 232q^{55} + 76q^{57} + 66q^{58} - 36q^{60} - 140q^{61} - 206q^{63} - 346q^{64} + 398q^{66} + 204q^{67} + 80q^{70} + 384q^{72} - 224q^{73} - 80q^{75} + 100q^{76} - 341q^{78} - 344q^{79} - 232q^{81} - 62q^{82} - 330q^{84} + 480q^{85} + 86q^{87} + 436q^{88} - 514q^{90} - 172q^{91} + 62q^{93} + 514q^{94} + 609q^{96} - 24q^{97} + 234q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(69, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
69.3.b.a \(14\) \(1.880\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(-4\) \(0\) \(-4\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)