Properties

Label 144.2.a
Level 144
Weight 2
Character orbit a
Rep. character \(\chi_{144}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 2
Sturm bound 48
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(144))\).

Total New Old
Modular forms 36 3 33
Cusp forms 13 2 11
Eisenstein series 23 1 22

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

\(2\)\(3\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2q + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 2q + 2q^{5} + 4q^{7} + 4q^{11} - 2q^{17} - 4q^{19} - 8q^{23} - 6q^{25} - 6q^{29} - 4q^{31} - 4q^{37} + 6q^{41} - 12q^{43} + 2q^{49} + 2q^{53} + 8q^{55} + 4q^{59} + 12q^{61} - 4q^{65} + 20q^{67} + 8q^{71} + 12q^{79} - 4q^{83} - 4q^{85} + 6q^{89} + 8q^{91} + 8q^{95} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(144))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
144.2.a.a \(1\) \(1.150\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(q+4q^{7}+2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots\)
144.2.a.b \(1\) \(1.150\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(q+2q^{5}+4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(144)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))
$7$ (\( 1 - 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))
$13$ (\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))
$17$ (\( 1 + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))
$19$ (\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))
$29$ (\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))
$37$ (\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))
$41$ (\( 1 + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))
$43$ (\( 1 + 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))
$53$ (\( 1 + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))
$61$ (\( 1 - 14 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))
$67$ (\( 1 - 16 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))
$73$ (\( 1 + 10 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))
$79$ (\( 1 - 4 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))
$83$ (\( 1 + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))
$89$ (\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))
$97$ (\( 1 - 14 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))
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