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Properties

Label 129.3.b
Level $129$
Weight $3$
Character orbit 129.b
Rep. character $\chi_{129}(85,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $1$
Sturm bound $44$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 129 = 3 \cdot 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 129.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(44\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(129, [\chi])\).

Total New Old
Modular forms 32 14 18
Cusp forms 28 14 14
Eisenstein series 4 0 4

Trace form

\( 14 q - 36 q^{4} - 42 q^{9} + O(q^{10}) \) \( 14 q - 36 q^{4} - 42 q^{9} + 8 q^{10} - 14 q^{11} - 2 q^{13} - 12 q^{14} - 12 q^{15} + 172 q^{16} - 18 q^{17} - 48 q^{21} + 150 q^{23} - 34 q^{25} + 62 q^{31} - 236 q^{35} + 108 q^{36} - 172 q^{38} - 224 q^{40} - 50 q^{41} + 46 q^{43} + 44 q^{44} + 152 q^{47} - 10 q^{49} + 112 q^{52} + 270 q^{53} + 300 q^{56} - 120 q^{57} - 496 q^{58} - 244 q^{59} + 276 q^{60} - 380 q^{64} - 216 q^{66} + 134 q^{67} + 768 q^{68} - 80 q^{74} - 132 q^{78} - 60 q^{79} + 126 q^{81} - 294 q^{83} + 312 q^{84} + 468 q^{86} + 252 q^{87} - 24 q^{90} - 880 q^{92} + 140 q^{95} - 480 q^{96} + 534 q^{97} + 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(129, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
129.3.b.a 129.b 43.b $14$ $3.515$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(-3+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(129, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(129, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 2}\)