↑

Properties

Label 129.2.a
Level $129$
Weight $2$
Character orbit 129.a
Rep. character $\chi_{129}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $4$
Sturm bound $29$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 129 = 3 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 129.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(29\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(129))\).

Total New Old
Modular forms 16 7 9
Cusp forms 13 7 6
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.

\(3\)\(43\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(2\)
\(-\)\(+\)$-$\(4\)
Plus space\(+\)\(1\)
Minus space\(-\)\(6\)

Trace form

\( 7 q + q^{2} + q^{3} + 7 q^{4} - 2 q^{5} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 7 q^{9} + O(q^{10}) \) \( 7 q + q^{2} + q^{3} + 7 q^{4} - 2 q^{5} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 7 q^{9} - 10 q^{10} + 2 q^{11} + 7 q^{12} - 4 q^{14} - 2 q^{15} + 19 q^{16} - 12 q^{17} + q^{18} - 10 q^{20} + 4 q^{21} - 16 q^{22} + 18 q^{23} - 15 q^{24} - 3 q^{25} - 18 q^{26} + q^{27} - 16 q^{28} + 2 q^{29} - 6 q^{30} + 6 q^{31} - 35 q^{32} - 14 q^{34} + 4 q^{35} + 7 q^{36} + 6 q^{37} + 14 q^{39} - 18 q^{40} - 20 q^{41} + 8 q^{42} - 3 q^{43} + 32 q^{44} - 2 q^{45} + 12 q^{46} - 8 q^{47} - q^{48} - 5 q^{49} + 31 q^{50} + 2 q^{51} + 10 q^{52} - 4 q^{53} - 3 q^{54} + 36 q^{55} + 28 q^{56} - 2 q^{58} + 24 q^{59} - 6 q^{60} - 18 q^{61} + 40 q^{62} + 4 q^{63} + 19 q^{64} - 32 q^{65} - 20 q^{66} - 26 q^{67} - 22 q^{68} - 4 q^{69} - 8 q^{70} + 28 q^{71} - 3 q^{72} + 2 q^{73} + 6 q^{74} + 7 q^{75} + 4 q^{76} + 4 q^{77} + 2 q^{78} + 8 q^{79} + 22 q^{80} + 7 q^{81} + 58 q^{82} - 6 q^{83} + 4 q^{84} - 8 q^{85} + 3 q^{86} - 10 q^{87} - 48 q^{88} - 14 q^{89} - 10 q^{90} - 4 q^{91} + 88 q^{92} + 12 q^{94} + 12 q^{95} - 23 q^{96} - 4 q^{97} - 31 q^{98} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(129))\) 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 43
129.2.a.a 129.a 1.a $1$ $1.030$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-2q^{5}-2q^{7}+q^{9}-5q^{11}+\cdots\)
129.2.a.b 129.a 1.a $1$ $1.030$ \(\Q\) None \(1\) \(1\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots\)
129.2.a.c 129.a 1.a $2$ $1.030$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
129.2.a.d 129.a 1.a $3$ $1.030$ 3.3.568.1 None \(-2\) \(3\) \(-4\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(129))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(129)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 2}\)