Properties

Label 224.1.r
Level 224
Weight 1
Character orbit r
Rep. character \(\chi_{224}(95,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newform subspaces 1
Sturm bound 32
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 224.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(224, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4q - 2q^{5} + O(q^{10}) \) \( 4q - 2q^{5} - 2q^{17} - 2q^{21} - 2q^{33} + 2q^{37} - 4q^{49} + 2q^{53} - 4q^{57} + 2q^{61} + 4q^{69} + 2q^{73} + 2q^{77} + 2q^{81} + 4q^{85} + 2q^{89} - 2q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.1.r.a \(4\) \(0.112\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)

Hecke characteristic polynomials

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