Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 44.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(44))\) into newform subspaces

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - T + 3 T^{2} \)
$5$ \( 1 + 3 T + 5 T^{2} \)
$7$ \( 1 - 2 T + 7 T^{2} \)
$11$ \( 1 + T \)
$13$ \( 1 + 4 T + 13 T^{2} \)
$17$ \( 1 - 6 T + 17 T^{2} \)
$19$ \( 1 - 8 T + 19 T^{2} \)
$23$ \( 1 + 3 T + 23 T^{2} \)
$29$ \( 1 + 29 T^{2} \)
$31$ \( 1 - 5 T + 31 T^{2} \)
$37$ \( 1 + T + 37 T^{2} \)
$41$ \( 1 + 41 T^{2} \)
$43$ \( 1 + 10 T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 + 6 T + 53 T^{2} \)
$59$ \( 1 - 3 T + 59 T^{2} \)
$61$ \( 1 + 4 T + 61 T^{2} \)
$67$ \( 1 + T + 67 T^{2} \)
$71$ \( 1 - 15 T + 71 T^{2} \)
$73$ \( 1 + 4 T + 73 T^{2} \)
$79$ \( 1 - 2 T + 79 T^{2} \)
$83$ \( 1 - 6 T + 83 T^{2} \)
$89$ \( 1 + 9 T + 89 T^{2} \)
$97$ \( 1 + 7 T + 97 T^{2} \)
show more
show less