Properties

Label 84.1.p
Level 84
Weight 1
Character orbit p
Rep. character \(\chi_{84}(53,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newform subspaces 1
Sturm bound 16
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 84.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(84, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

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

\( 2q - q^{3} - q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - q^{7} - q^{9} - 2q^{13} + q^{19} + 2q^{21} - q^{25} + 2q^{27} + q^{31} + q^{37} + q^{39} - 2q^{43} - q^{49} - 2q^{57} - 2q^{61} - q^{63} + q^{67} + q^{73} - q^{75} + q^{79} - q^{81} + q^{91} + q^{93} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
84.1.p.a \(2\) \(0.042\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)

Hecke characteristic polynomials

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