Properties

Label 144.4.a
Level $144$
Weight $4$
Character orbit 144.a
Rep. character $\chi_{144}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $7$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 144.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(144))\).

Total New Old
Modular forms 84 8 76
Cusp forms 60 7 53
Eisenstein series 24 1 23

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.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(3\)

Trace form

\( 7 q + 12 q^{7} + O(q^{10}) \) \( 7 q + 12 q^{7} - 24 q^{11} + 22 q^{13} - 24 q^{17} + 160 q^{19} + 192 q^{23} + 197 q^{25} + 144 q^{29} - 164 q^{31} - 624 q^{35} - 30 q^{37} - 216 q^{41} + 464 q^{43} + 1104 q^{47} - 241 q^{49} - 240 q^{53} - 1168 q^{55} - 1416 q^{59} - 518 q^{61} + 672 q^{65} + 904 q^{67} + 2016 q^{71} - 614 q^{73} + 288 q^{77} - 2404 q^{79} - 2952 q^{83} + 992 q^{85} - 648 q^{89} + 1176 q^{91} + 3120 q^{95} - 430 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(144))\) 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
144.4.a.a 144.a 1.a $1$ $8.496$ \(\Q\) None \(0\) \(0\) \(-16\) \(12\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{5}+12q^{7}+2^{6}q^{11}+58q^{13}+\cdots\)
144.4.a.b 144.a 1.a $1$ $8.496$ \(\Q\) None \(0\) \(0\) \(-14\) \(24\) $+$ $-$ $\mathrm{SU}(2)$ \(q-14q^{5}+24q^{7}-28q^{11}-74q^{13}+\cdots\)
144.4.a.c 144.a 1.a $1$ $8.496$ \(\Q\) None \(0\) \(0\) \(-6\) \(16\) $-$ $-$ $\mathrm{SU}(2)$ \(q-6q^{5}+2^{4}q^{7}+12q^{11}+38q^{13}+\cdots\)
144.4.a.d 144.a 1.a $1$ $8.496$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-20\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-20q^{7}-70q^{13}-56q^{19}-5^{3}q^{25}+\cdots\)
144.4.a.e 144.a 1.a $1$ $8.496$ \(\Q\) None \(0\) \(0\) \(2\) \(-24\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-24q^{7}-44q^{11}+22q^{13}+\cdots\)
144.4.a.f 144.a 1.a $1$ $8.496$ \(\Q\) None \(0\) \(0\) \(16\) \(12\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{5}+12q^{7}-2^{6}q^{11}+58q^{13}+\cdots\)
144.4.a.g 144.a 1.a $1$ $8.496$ \(\Q\) None \(0\) \(0\) \(18\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+18q^{5}-8q^{7}+6^{2}q^{11}-10q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(144)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)