Properties

Label 119.2.b
Level $119$
Weight $2$
Character orbit 119.b
Rep. character $\chi_{119}(50,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 119 = 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 119.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(119, [\chi])\).

Total New Old
Modular forms 14 10 4
Cusp forms 10 10 0
Eisenstein series 4 0 4

Trace form

\( 10 q - 4 q^{2} + 4 q^{4} - 12 q^{8} - 6 q^{9} + O(q^{10}) \) \( 10 q - 4 q^{2} + 4 q^{4} - 12 q^{8} - 6 q^{9} - 8 q^{13} - 8 q^{15} + 8 q^{16} + 2 q^{17} + 12 q^{18} + 4 q^{19} - 2 q^{25} + 12 q^{26} + 10 q^{30} - 18 q^{32} - 20 q^{33} + 6 q^{34} + 8 q^{35} + 10 q^{36} - 4 q^{38} - 14 q^{42} + 16 q^{43} - 10 q^{49} + 6 q^{50} - 64 q^{52} + 8 q^{53} - 12 q^{55} + 56 q^{59} - 26 q^{60} + 72 q^{66} + 24 q^{67} - 22 q^{68} + 28 q^{69} + 4 q^{70} + 10 q^{72} - 12 q^{76} + 2 q^{81} - 12 q^{83} + 24 q^{84} - 20 q^{85} - 74 q^{86} - 52 q^{87} - 4 q^{89} + 32 q^{93} - 20 q^{94} + 4 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(119, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
119.2.b.a 119.b 17.b $10$ $0.950$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{8})q^{3}+(-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)