Properties

Label 44.1.d
Level 44
Weight 1
Character orbit d
Rep. character \(\chi_{44}(21,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(44, [\chi])\) into irreducible Hecke orbits

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 \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots\)