Properties

Label 44.1.d
Level 44
Weight 1
Character orbit d
Rep. character \(\chi_{44}(21,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 44.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(44, [\chi])\).

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

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

\( q - q^{3} - q^{5} + O(q^{10}) \) \( q - q^{3} - q^{5} + q^{11} + q^{15} - q^{23} + q^{27} - q^{31} - q^{33} - q^{37} + 2q^{47} + q^{49} + 2q^{53} - q^{55} - q^{59} - q^{67} + q^{69} - q^{71} - q^{81} - q^{89} + q^{93} - q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(44, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
44.1.d.a \(1\) \(0.022\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots\)

Hecke characteristic polynomials

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