Properties

Label 144.8.a
Level $144$
Weight $8$
Character orbit 144.a
Rep. character $\chi_{144}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $14$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 144.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(144))\).

Total New Old
Modular forms 180 18 162
Cusp forms 156 17 139
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
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(9\)
Minus space\(-\)\(8\)

Trace form

\( 17 q + 140 q^{5} - 1348 q^{7} + O(q^{10}) \) \( 17 q + 140 q^{5} - 1348 q^{7} - 3392 q^{11} - 3278 q^{13} + 11260 q^{17} - 136 q^{19} - 78992 q^{23} + 240587 q^{25} - 7956 q^{29} - 62884 q^{31} + 31536 q^{35} - 228482 q^{37} + 133452 q^{41} - 94408 q^{43} - 23184 q^{47} + 2420169 q^{49} + 615164 q^{53} + 672672 q^{55} - 526736 q^{59} - 271802 q^{61} - 834328 q^{65} + 5292224 q^{67} + 2617712 q^{71} - 188498 q^{73} + 1831008 q^{77} + 656060 q^{79} - 4232800 q^{83} + 9182472 q^{85} - 10976772 q^{89} + 21664888 q^{91} + 10625120 q^{95} + 392278 q^{97} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(144))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
144.8.a.a 144.a 1.a $1$ $44.983$ \(\Q\) None 8.8.a.b \(0\) \(0\) \(-430\) \(1224\) $+$ $-$ $\mathrm{SU}(2)$ \(q-430q^{5}+1224q^{7}-3164q^{11}+\cdots\)
144.8.a.b 144.a 1.a $1$ $44.983$ \(\Q\) None 3.8.a.a \(0\) \(0\) \(-390\) \(64\) $-$ $-$ $\mathrm{SU}(2)$ \(q-390q^{5}+2^{6}q^{7}-948q^{11}-5098q^{13}+\cdots\)
144.8.a.c 144.a 1.a $1$ $44.983$ \(\Q\) None 12.8.a.b \(0\) \(0\) \(-270\) \(-1112\) $-$ $-$ $\mathrm{SU}(2)$ \(q-270q^{5}-1112q^{7}-5724q^{11}+\cdots\)
144.8.a.d 144.a 1.a $1$ $44.983$ \(\Q\) None 24.8.a.c \(0\) \(0\) \(-110\) \(-504\) $+$ $-$ $\mathrm{SU}(2)$ \(q-110q^{5}-504q^{7}+3812q^{11}+9574q^{13}+\cdots\)
144.8.a.e 144.a 1.a $1$ $44.983$ \(\Q\) \(\Q(\sqrt{-3}) \) 36.8.a.b \(0\) \(0\) \(0\) \(508\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+508q^{7}-14614q^{13}+57448q^{19}+\cdots\)
144.8.a.f 144.a 1.a $1$ $44.983$ \(\Q\) None 24.8.a.a \(0\) \(0\) \(26\) \(-1056\) $+$ $-$ $\mathrm{SU}(2)$ \(q+26q^{5}-1056q^{7}+6412q^{11}+5206q^{13}+\cdots\)
144.8.a.g 144.a 1.a $1$ $44.983$ \(\Q\) None 8.8.a.a \(0\) \(0\) \(82\) \(456\) $+$ $-$ $\mathrm{SU}(2)$ \(q+82q^{5}+456q^{7}-2524q^{11}-10778q^{13}+\cdots\)
144.8.a.h 144.a 1.a $1$ $44.983$ \(\Q\) None 6.8.a.a \(0\) \(0\) \(114\) \(1576\) $-$ $-$ $\mathrm{SU}(2)$ \(q+114q^{5}+1576q^{7}+7332q^{11}+\cdots\)
144.8.a.i 144.a 1.a $1$ $44.983$ \(\Q\) None 2.8.a.a \(0\) \(0\) \(210\) \(-1016\) $-$ $-$ $\mathrm{SU}(2)$ \(q+210q^{5}-1016q^{7}+1092q^{11}+\cdots\)
144.8.a.j 144.a 1.a $1$ $44.983$ \(\Q\) None 12.8.a.a \(0\) \(0\) \(378\) \(832\) $-$ $-$ $\mathrm{SU}(2)$ \(q+378q^{5}+832q^{7}-2484q^{11}+14870q^{13}+\cdots\)
144.8.a.k 144.a 1.a $1$ $44.983$ \(\Q\) None 24.8.a.b \(0\) \(0\) \(530\) \(-120\) $+$ $-$ $\mathrm{SU}(2)$ \(q+530q^{5}-120q^{7}-7196q^{11}-9626q^{13}+\cdots\)
144.8.a.l 144.a 1.a $2$ $44.983$ \(\Q(\sqrt{46}) \) None 72.8.a.f \(0\) \(0\) \(-224\) \(-840\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-112+\beta )q^{5}+(-420+4\beta )q^{7}+\cdots\)
144.8.a.m 144.a 1.a $2$ $44.983$ \(\Q(\sqrt{10}) \) None 9.8.a.b \(0\) \(0\) \(0\) \(-520\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-260q^{7}-20\beta q^{11}+6890q^{13}+\cdots\)
144.8.a.n 144.a 1.a $2$ $44.983$ \(\Q(\sqrt{46}) \) None 72.8.a.f \(0\) \(0\) \(224\) \(-840\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(112+\beta )q^{5}+(-420-4\beta )q^{7}+(320+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(144)) \simeq \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)