Properties

Label 55.1.d
Level 55
Weight 1
Character orbit d
Rep. character \(\chi_{55}(54,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 55.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(55, [\chi])\).

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

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{4} - q^{5} + q^{9} + O(q^{10}) \) \( q - q^{4} - q^{5} + q^{9} - q^{11} + q^{16} + q^{20} + q^{25} - 2q^{31} - q^{36} + q^{44} - q^{45} - q^{49} + q^{55} + 2q^{59} - q^{64} + 2q^{71} - q^{80} + q^{81} - 2q^{89} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
55.1.d.a \(1\) \(0.027\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\)

Hecke characteristic polynomials

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