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Properties

Label 119.2.a
Level $119$
Weight $2$
Character orbit 119.a
Rep. character $\chi_{119}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 119 = 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 119.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(119))\).

Total New Old
Modular forms 14 9 5
Cusp forms 11 9 2
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)\(17\)FrickeDim
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(4\)
Plus space\(+\)\(0\)
Minus space\(-\)\(9\)

Trace form

\( 9 q + q^{2} + 13 q^{4} + 2 q^{5} - q^{7} - 3 q^{8} + 17 q^{9} + O(q^{10}) \) \( 9 q + q^{2} + 13 q^{4} + 2 q^{5} - q^{7} - 3 q^{8} + 17 q^{9} + 2 q^{10} - 16 q^{12} + 10 q^{13} - 3 q^{14} - 8 q^{15} + 9 q^{16} + q^{17} - 19 q^{18} + 16 q^{19} - 22 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{23} - 24 q^{24} + 19 q^{25} - 30 q^{26} - 24 q^{27} - 7 q^{28} - 6 q^{29} - 46 q^{30} + 12 q^{31} - 5 q^{32} + 4 q^{33} + 3 q^{34} + 2 q^{35} + 19 q^{36} + 14 q^{37} - 8 q^{38} - 4 q^{39} + 22 q^{40} + 30 q^{41} + 2 q^{42} - 4 q^{43} + 8 q^{44} - 2 q^{45} + 32 q^{46} - 8 q^{47} - 12 q^{48} + 9 q^{49} + 25 q^{50} - 4 q^{51} + 30 q^{52} - 22 q^{53} + 28 q^{54} - 20 q^{55} - 15 q^{56} + 36 q^{57} - 10 q^{58} + 4 q^{59} + 10 q^{60} + 34 q^{61} + 32 q^{62} - 5 q^{63} + q^{64} - 4 q^{65} + 48 q^{66} + 4 q^{67} + 7 q^{68} - 20 q^{69} - 6 q^{70} - 16 q^{71} + 15 q^{72} + 30 q^{73} - 22 q^{74} - 44 q^{75} + 32 q^{76} + 4 q^{77} + 12 q^{78} + 4 q^{79} - 14 q^{80} + 33 q^{81} - 14 q^{82} - 40 q^{83} + 28 q^{84} - 2 q^{85} + 50 q^{86} - 28 q^{87} - 68 q^{88} + 10 q^{89} + 70 q^{90} + 6 q^{91} + 32 q^{92} - 48 q^{93} - 20 q^{94} - 36 q^{95} + 38 q^{97} + q^{98} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(119))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 17
119.2.a.a 119.a 1.a $4$ $0.950$ 4.4.9301.1 None \(-1\) \(2\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
119.2.a.b 119.a 1.a $5$ $0.950$ 5.5.453749.1 None \(2\) \(-2\) \(0\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(119))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(119)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)