Properties

Label 144.2.a
Level $144$
Weight $2$
Character orbit 144.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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
144.2.a.a 144.a 1.a $1$ $1.150$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+4q^{7}+2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots\)
144.2.a.b 144.a 1.a $1$ $1.150$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)

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

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