Properties

Label 72.14.a
Level $72$
Weight $14$
Character orbit 72.a
Rep. character $\chi_{72}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $8$
Sturm bound $168$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 72.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(72))\).

Total New Old
Modular forms 164 16 148
Cusp forms 148 16 132
Eisenstein series 16 0 16

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
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(3\)
\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(8\)
Minus space\(-\)\(8\)

Trace form

\( 16 q + 45396 q^{5} + 29064 q^{7} + O(q^{10}) \) \( 16 q + 45396 q^{5} + 29064 q^{7} - 5029128 q^{11} + 16094584 q^{13} + 1786284 q^{17} + 597489512 q^{19} + 421440912 q^{23} + 5189153624 q^{25} - 1464068988 q^{29} - 4641056104 q^{31} - 16796644992 q^{35} - 37601177856 q^{37} - 12731964228 q^{41} - 47694177032 q^{43} + 3458822400 q^{47} + 383446429808 q^{49} + 109401913620 q^{53} + 222753221488 q^{55} + 344001682296 q^{59} - 601091200064 q^{61} - 513334877544 q^{65} - 1918401530344 q^{67} + 416079972720 q^{71} - 1745725305944 q^{73} - 603188475264 q^{77} + 2862376781944 q^{79} - 587288394360 q^{83} + 7541995342808 q^{85} + 3301156233468 q^{89} + 7073230080144 q^{91} - 9753652546704 q^{95} + 2482183898984 q^{97} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(72))\) 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
72.14.a.a 72.a 1.a $1$ $77.206$ \(\Q\) None \(0\) \(0\) \(4330\) \(-139992\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4330q^{5}-139992q^{7}+6484324q^{11}+\cdots\)
72.14.a.b 72.a 1.a $1$ $77.206$ \(\Q\) None \(0\) \(0\) \(22490\) \(181272\) $+$ $-$ $\mathrm{SU}(2)$ \(q+22490q^{5}+181272q^{7}+9261428q^{11}+\cdots\)
72.14.a.c 72.a 1.a $2$ $77.206$ \(\Q(\sqrt{781}) \) None \(0\) \(0\) \(-18476\) \(110928\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-9238-4\beta )q^{5}+(55464-74\beta )q^{7}+\cdots\)
72.14.a.d 72.a 1.a $2$ $77.206$ \(\Q(\sqrt{62869}) \) None \(0\) \(0\) \(-5068\) \(104880\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2534-\beta )q^{5}+(52440+5\beta )q^{7}+\cdots\)
72.14.a.e 72.a 1.a $2$ $77.206$ \(\Q(\sqrt{1621}) \) None \(0\) \(0\) \(11204\) \(275808\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(5602-\beta )q^{5}+(137904-13\beta )q^{7}+\cdots\)
72.14.a.f 72.a 1.a $2$ $77.206$ \(\Q(\sqrt{406}) \) None \(0\) \(0\) \(30916\) \(-532896\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(15458+7\beta )q^{5}+(-266448-37\beta )q^{7}+\cdots\)
72.14.a.g 72.a 1.a $3$ $77.206$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(0\) \(-50256\) \(14532\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-16752+\beta _{2})q^{5}+(4844-\beta _{1}+\cdots)q^{7}+\cdots\)
72.14.a.h 72.a 1.a $3$ $77.206$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(0\) \(50256\) \(14532\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(16752-\beta _{2})q^{5}+(4844-\beta _{1}-3\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(72))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(72)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)