Properties

Label 44.2.a
Level 44
Weight 2
Character orbit a
Rep. character \(\chi_{44}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 44.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(44))\).

Total New Old
Modular forms 9 1 8
Cusp forms 4 1 3
Eisenstein series 5 0 5

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(11\)FrickeDim.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\(q \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut q^{33} \) \(\mathstrut -\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 3q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut +\mathstrut 3q^{55} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut q^{67} \) \(\mathstrut -\mathstrut 3q^{69} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 4q^{73} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut +\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 18q^{85} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 5q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut -\mathstrut 7q^{97} \) \(\mathstrut +\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(44))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11
44.2.a.a \(1\) \(0.351\) \(\Q\) None \(0\) \(1\) \(-3\) \(2\) \(-\) \(+\) \(q+q^{3}-3q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(44))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(44)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)