Properties

Label 127.1.b
Level 127
Weight 1
Character orbit b
Rep. character \(\chi_{127}(126,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 10
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 127 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 127.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 127 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(127, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - q^{2} + q^{4} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{4} - 2q^{8} + 2q^{9} - q^{11} - q^{13} - q^{17} - q^{18} - q^{19} - 2q^{22} + 2q^{25} - 2q^{26} - q^{31} + 2q^{32} + 3q^{34} + q^{36} - q^{37} + 3q^{38} - q^{41} + 2q^{44} - q^{47} + 2q^{49} - q^{50} + 2q^{52} - q^{61} + 3q^{62} - q^{64} - 3q^{68} - q^{71} - 2q^{72} - q^{73} + 3q^{74} - 3q^{76} - q^{79} + 2q^{81} - 2q^{82} + q^{88} - 2q^{94} - q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(127, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
127.1.b.a \(2\) \(0.063\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-127}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$3$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$5$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$7$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$11$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$13$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$17$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$19$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$23$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$29$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$31$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$37$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$41$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$43$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$47$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$53$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$59$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$61$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$67$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$71$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$73$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$79$ \( 1 + T + T^{2} + T^{3} + T^{4} \)
$83$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$89$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$97$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
show more
show less