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Properties

Label 119.2.j
Level $119$
Weight $2$
Character orbit 119.j
Rep. character $\chi_{119}(16,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{6})\)
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 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20 q - 2 q^{2} - 10 q^{4} + O(q^{10}) \) \( 20 q - 2 q^{2} - 10 q^{4} - 16 q^{13} - 16 q^{15} - 2 q^{16} - 2 q^{17} + 18 q^{18} - 10 q^{19} + 12 q^{21} - 10 q^{25} + 12 q^{26} - 10 q^{30} - 12 q^{32} + 2 q^{33} + 24 q^{34} - 26 q^{35} + 56 q^{36} - 2 q^{38} - 16 q^{42} - 52 q^{43} + 30 q^{47} + 4 q^{49} + 6 q^{51} - 2 q^{52} + 40 q^{53} + 12 q^{55} - 14 q^{59} - 22 q^{60} - 24 q^{64} + 12 q^{66} + 12 q^{67} - 32 q^{68} - 88 q^{69} - 34 q^{70} - 16 q^{72} + 132 q^{76} + 30 q^{77} - 2 q^{81} + 96 q^{83} + 18 q^{84} - 4 q^{85} - 10 q^{86} - 26 q^{87} + 16 q^{89} + 46 q^{93} + 50 q^{94} + 62 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.j.a 119.j 119.j $20$ $0.950$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{15}q^{2}-\beta _{1}q^{3}+(-1+\beta _{11}+\beta _{14}+\cdots)q^{4}+\cdots\)