↑

Properties

Label 127.2.a
Level $127$
Weight $2$
Character orbit 127.a
Rep. character $\chi_{127}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $21$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 127.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(127))\).

Total New Old
Modular forms 11 11 0
Cusp forms 10 10 0
Eisenstein series 1 1 0

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

\(127\)Dim
\(+\)\(3\)
\(-\)\(7\)

Trace form

\( 10 q - q^{2} + 9 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{7} - 3 q^{8} + 12 q^{9} + O(q^{10}) \) \( 10 q - q^{2} + 9 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{7} - 3 q^{8} + 12 q^{9} - 2 q^{10} - 4 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{15} - 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} + 14 q^{20} - 16 q^{21} + 6 q^{22} - 10 q^{23} - 6 q^{24} + 10 q^{25} + 2 q^{26} - 20 q^{28} - 4 q^{29} - 34 q^{30} + 4 q^{31} - 2 q^{32} - 2 q^{33} + 11 q^{34} + 16 q^{35} + q^{36} - 6 q^{37} + 23 q^{38} - 6 q^{40} + 2 q^{41} + 18 q^{42} - 10 q^{43} - 39 q^{44} + 16 q^{45} + 6 q^{46} + 22 q^{47} - 10 q^{48} - 12 q^{49} + 13 q^{50} + 38 q^{51} - 15 q^{52} + 32 q^{53} - 8 q^{54} - 26 q^{55} - 2 q^{57} - 40 q^{58} - 12 q^{59} + 4 q^{61} - 11 q^{62} - 4 q^{63} + 9 q^{64} - 6 q^{65} + 18 q^{66} - 28 q^{67} + 44 q^{68} + 24 q^{69} + 42 q^{70} + 10 q^{71} - 37 q^{72} + 16 q^{73} + 35 q^{74} + 12 q^{75} + 24 q^{76} + 16 q^{77} + 20 q^{78} - 14 q^{79} - 2 q^{80} - 14 q^{81} + 26 q^{82} + 38 q^{83} - 50 q^{84} + 54 q^{85} - 4 q^{86} - 20 q^{87} + 19 q^{88} - 20 q^{89} - 42 q^{90} - 52 q^{91} - 50 q^{92} - 4 q^{93} + 14 q^{94} - 40 q^{95} + 46 q^{96} - 20 q^{97} + q^{98} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(127))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 127
127.2.a.a 127.a 1.a $3$ $1.014$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(-6\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
127.2.a.b 127.a 1.a $7$ $1.014$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(3\) \(8\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{3}+\cdots\)