Properties

Label 144.12.a
Level $144$
Weight $12$
Character orbit 144.a
Rep. character $\chi_{144}(1,\cdot)$
Character field $\Q$
Dimension $27$
Newform subspaces $20$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 144.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(144))\).

Total New Old
Modular forms 276 28 248
Cusp forms 252 27 225
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
\(+\)\(+\)$+$\(6\)
\(+\)\(-\)$-$\(8\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(8\)
Plus space\(+\)\(14\)
Minus space\(-\)\(13\)

Trace form

\( 27 q - 1320 q^{5} + 34540 q^{7} + O(q^{10}) \) \( 27 q - 1320 q^{5} + 34540 q^{7} - 753576 q^{11} + 123022 q^{13} - 5026032 q^{17} + 904464 q^{19} + 23508384 q^{23} + 228744977 q^{25} + 9913992 q^{29} - 297288612 q^{31} - 229622064 q^{35} + 278490074 q^{37} - 255403536 q^{41} - 1029453088 q^{43} - 3603047280 q^{47} + 5325196291 q^{49} - 1021104216 q^{53} + 6010522192 q^{55} - 2054033112 q^{59} + 36009682 q^{61} - 5273223888 q^{65} + 12198246840 q^{67} + 11212433280 q^{71} - 25696031678 q^{73} - 41238780000 q^{77} + 37173709532 q^{79} + 35144598792 q^{83} - 8657557328 q^{85} + 85477639680 q^{89} - 43220744872 q^{91} - 56089889520 q^{95} + 22720269402 q^{97} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(144))\) 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
144.12.a.a 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(-9990\) \(86128\) $-$ $-$ $\mathrm{SU}(2)$ \(q-9990q^{5}+86128q^{7}-806004q^{11}+\cdots\)
144.12.a.b 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(-5766\) \(-72464\) $-$ $-$ $\mathrm{SU}(2)$ \(q-5766q^{5}-72464q^{7}-408948q^{11}+\cdots\)
144.12.a.c 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(-5280\) \(49036\) $-$ $+$ $\mathrm{SU}(2)$ \(q-5280q^{5}+49036q^{7}+414336q^{11}+\cdots\)
144.12.a.d 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(-4830\) \(16744\) $-$ $-$ $\mathrm{SU}(2)$ \(q-4830q^{5}+16744q^{7}+534612q^{11}+\cdots\)
144.12.a.e 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(-3630\) \(-32936\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3630q^{5}-32936q^{7}-758748q^{11}+\cdots\)
144.12.a.f 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(-2862\) \(-9128\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2862q^{5}-9128q^{7}+668196q^{11}+\cdots\)
144.12.a.g 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(-1870\) \(72312\) $+$ $-$ $\mathrm{SU}(2)$ \(q-1870q^{5}+72312q^{7}+147940q^{11}+\cdots\)
144.12.a.h 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(-1190\) \(-18480\) $+$ $-$ $\mathrm{SU}(2)$ \(q-1190q^{5}-18480q^{7}+135884q^{11}+\cdots\)
144.12.a.i 144.a 1.a $1$ $110.641$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(268\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+268q^{7}-134374q^{13}+4655368q^{19}+\cdots\)
144.12.a.j 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(3490\) \(55464\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3490q^{5}+55464q^{7}-597004q^{11}+\cdots\)
144.12.a.k 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(5280\) \(49036\) $-$ $+$ $\mathrm{SU}(2)$ \(q+5280q^{5}+49036q^{7}-414336q^{11}+\cdots\)
144.12.a.l 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(5370\) \(27760\) $-$ $-$ $\mathrm{SU}(2)$ \(q+5370q^{5}+27760q^{7}+637836q^{11}+\cdots\)
144.12.a.m 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(7130\) \(19536\) $+$ $-$ $\mathrm{SU}(2)$ \(q+7130q^{5}+19536q^{7}-196148q^{11}+\cdots\)
144.12.a.n 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(10530\) \(-49304\) $-$ $-$ $\mathrm{SU}(2)$ \(q+10530q^{5}-49304q^{7}-309420q^{11}+\cdots\)
144.12.a.o 144.a 1.a $1$ $110.641$ \(\Q\) None \(0\) \(0\) \(11730\) \(50008\) $-$ $-$ $\mathrm{SU}(2)$ \(q+11730q^{5}+50008q^{7}-531420q^{11}+\cdots\)
144.12.a.p 144.a 1.a $2$ $110.641$ \(\Q(\sqrt{109}) \) None \(0\) \(0\) \(-7868\) \(-91056\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-3934-4\beta )q^{5}+(-45528+14\beta )q^{7}+\cdots\)
144.12.a.q 144.a 1.a $2$ $110.641$ \(\Q(\sqrt{3061}) \) None \(0\) \(0\) \(-1564\) \(-37776\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-782-\beta )q^{5}+(-18888+\beta )q^{7}+\cdots\)
144.12.a.r 144.a 1.a $2$ $110.641$ \(\Q(\sqrt{70}) \) None \(0\) \(0\) \(0\) \(-116200\) $-$ $+$ $\mathrm{SU}(2)$ \(q+7\beta q^{5}-58100q^{7}+10^{2}\beta q^{11}+\cdots\)
144.12.a.s 144.a 1.a $3$ $110.641$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(0\) \(-1584\) \(17796\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-528-\beta _{1})q^{5}+(5932+\beta _{1}+\beta _{2})q^{7}+\cdots\)
144.12.a.t 144.a 1.a $3$ $110.641$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(0\) \(1584\) \(17796\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(528+\beta _{1})q^{5}+(5932+\beta _{1}+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(144)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)