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 $1$

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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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 127
127.2.a.a \(3\) \(1.014\) \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(-6\) \(-3\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
127.2.a.b \(7\) \(1.014\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(3\) \(8\) \(-3\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{3}+\cdots\)