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Properties

Label 159.2.a
Level $159$
Weight $2$
Character orbit 159.a
Rep. character $\chi_{159}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 159 = 3 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 159.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(159))\).

Total New Old
Modular forms 20 9 11
Cusp forms 17 9 8
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.

\(3\)\(53\)FrickeDim
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(4\)
Plus space\(+\)\(0\)
Minus space\(-\)\(9\)

Trace form

\( 9 q + 3 q^{2} - q^{3} + 13 q^{4} + 2 q^{5} + 3 q^{6} + 3 q^{8} + 9 q^{9} + O(q^{10}) \) \( 9 q + 3 q^{2} - q^{3} + 13 q^{4} + 2 q^{5} + 3 q^{6} + 3 q^{8} + 9 q^{9} - 2 q^{10} + 8 q^{11} - 7 q^{12} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 9 q^{16} + 10 q^{17} + 3 q^{18} - 4 q^{19} - 22 q^{20} - 8 q^{21} - 16 q^{22} - 4 q^{23} + 3 q^{24} + 19 q^{25} - 22 q^{26} - q^{27} - 32 q^{28} + 26 q^{29} - 18 q^{30} - 4 q^{31} - 21 q^{32} + 4 q^{33} - 34 q^{34} - 24 q^{35} + 13 q^{36} - 6 q^{37} - 44 q^{38} - 14 q^{39} - 32 q^{40} + 30 q^{41} - 6 q^{42} - 4 q^{43} + 4 q^{44} + 2 q^{45} + 26 q^{46} - 4 q^{47} - 15 q^{48} + 29 q^{49} + 17 q^{50} + 10 q^{51} + 12 q^{52} + q^{53} + 3 q^{54} - 20 q^{55} + 28 q^{56} - 8 q^{57} + 2 q^{58} - 8 q^{59} - 8 q^{60} + 26 q^{61} + q^{64} + 40 q^{65} + 20 q^{66} + 22 q^{68} + 8 q^{69} + 18 q^{70} - 4 q^{71} + 3 q^{72} + 18 q^{73} + 14 q^{74} - 7 q^{75} - 4 q^{76} - 12 q^{77} + 6 q^{78} + 8 q^{79} - 22 q^{80} + 9 q^{81} + 28 q^{82} - 24 q^{83} - 8 q^{84} + 36 q^{86} - 14 q^{87} + 12 q^{88} + 22 q^{89} - 2 q^{90} - 16 q^{91} + 44 q^{92} - 20 q^{93} + 16 q^{94} + 8 q^{95} + 29 q^{96} - 10 q^{97} + 19 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(159))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 53
159.2.a.a 159.a 1.a $4$ $1.270$ 4.4.1957.1 None \(3\) \(4\) \(2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+q^{3}+(1-\beta _{1}-\beta _{3})q^{4}+\cdots\)
159.2.a.b 159.a 1.a $5$ $1.270$ 5.5.1054013.1 None \(0\) \(-5\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{3})q^{2}-q^{3}+(2-\beta _{4})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(159))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(159)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 2}\)