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Properties

Label 69.3.d
Level $69$
Weight $3$
Character orbit 69.d
Rep. character $\chi_{69}(22,\cdot)$
Character field $\Q$
Dimension $8$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
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 8 10
Cusp forms 14 8 6
Eisenstein series 4 0 4

Trace form

\( 8 q - 4 q^{2} + 12 q^{6} + 4 q^{8} + 24 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{2} + 12 q^{6} + 4 q^{8} + 24 q^{9} - 8 q^{13} - 56 q^{16} - 12 q^{18} + 52 q^{23} + 12 q^{24} - 112 q^{25} - 152 q^{26} + 104 q^{29} + 16 q^{31} + 12 q^{32} + 96 q^{35} - 48 q^{39} + 32 q^{41} + 160 q^{46} + 152 q^{47} - 96 q^{48} - 256 q^{49} + 44 q^{50} + 264 q^{52} + 36 q^{54} + 192 q^{55} + 152 q^{58} - 160 q^{59} - 392 q^{62} - 64 q^{64} + 108 q^{69} - 168 q^{70} + 80 q^{71} + 12 q^{72} + 64 q^{73} - 72 q^{75} - 504 q^{77} + 144 q^{78} + 72 q^{81} + 248 q^{82} - 24 q^{85} - 192 q^{87} - 132 q^{92} - 24 q^{93} - 280 q^{94} - 336 q^{95} - 324 q^{96} + 548 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
69.3.d.a 69.d 23.b $8$ $1.880$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(69, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(69, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)