Properties

Label 69.6.c
Level $69$
Weight $6$
Character orbit 69.c
Rep. character $\chi_{69}(68,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(69, [\chi])\).

Total New Old
Modular forms 42 42 0
Cusp forms 38 38 0
Eisenstein series 4 4 0

Trace form

\( 38q - 600q^{4} - 75q^{6} - 444q^{9} + O(q^{10}) \) \( 38q - 600q^{4} - 75q^{6} - 444q^{9} - 159q^{12} + 520q^{13} + 11080q^{16} - 981q^{18} + 4164q^{24} + 17282q^{25} - 1140q^{27} + 6544q^{31} - 12165q^{36} - 45216q^{39} + 54328q^{46} - 4797q^{48} - 106822q^{49} - 33270q^{52} - 38628q^{54} - 139296q^{55} + 121706q^{58} - 12466q^{64} - 113580q^{69} + 37176q^{70} + 245904q^{72} - 93896q^{73} + 249840q^{75} + 305247q^{78} - 339372q^{81} - 112546q^{82} + 259584q^{85} + 126936q^{87} - 165666q^{93} - 40258q^{94} + 643173q^{96} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(69, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
69.6.c.a \(6\) \(11.066\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-3\beta _{2}-2\beta _{3}+\beta _{4}+\beta _{5})q^{2}+\cdots\)
69.6.c.b \(32\) \(11.066\) None \(0\) \(0\) \(0\) \(0\)