Properties

Label 44.1.d
Level $44$
Weight $1$
Character orbit 44.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

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

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

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
44.1.d.a 44.d 11.b $1$ $0.022$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-11}) \) None 44.1.d.a \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots\)