Properties

Label 432.6.a
Level $432$
Weight $6$
Character orbit 432.a
Rep. character $\chi_{432}(1,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $24$
Sturm bound $432$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(432\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(432))\).

Total New Old
Modular forms 378 40 338
Cusp forms 342 40 302
Eisenstein series 36 0 36

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
\(+\)\(+\)$+$\(9\)
\(+\)\(-\)$-$\(11\)
\(-\)\(+\)$-$\(10\)
\(-\)\(-\)$+$\(10\)
Plus space\(+\)\(19\)
Minus space\(-\)\(21\)

Trace form

\( 40 q + 62 q^{7} + O(q^{10}) \) \( 40 q + 62 q^{7} - 2798 q^{19} + 26364 q^{25} - 7916 q^{31} - 15056 q^{37} - 36648 q^{43} + 79528 q^{49} - 35204 q^{55} + 49224 q^{61} - 34718 q^{67} + 29568 q^{73} + 161142 q^{79} + 185392 q^{85} + 184222 q^{91} + 3800 q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(432))\) 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
432.6.a.a 432.a 1.a $1$ $69.286$ \(\Q\) None \(0\) \(0\) \(-84\) \(193\) $-$ $+$ $\mathrm{SU}(2)$ \(q-84q^{5}+193q^{7}+348q^{11}+845q^{13}+\cdots\)
432.6.a.b 432.a 1.a $1$ $69.286$ \(\Q\) None \(0\) \(0\) \(-33\) \(-59\) $-$ $+$ $\mathrm{SU}(2)$ \(q-33q^{5}-59q^{7}+147q^{11}+836q^{13}+\cdots\)
432.6.a.c 432.a 1.a $1$ $69.286$ \(\Q\) None \(0\) \(0\) \(-29\) \(-201\) $+$ $-$ $\mathrm{SU}(2)$ \(q-29q^{5}-201q^{7}-43q^{11}+244q^{13}+\cdots\)
432.6.a.d 432.a 1.a $1$ $69.286$ \(\Q\) None \(0\) \(0\) \(-24\) \(-77\) $-$ $-$ $\mathrm{SU}(2)$ \(q-24q^{5}-77q^{7}+408q^{11}+89q^{13}+\cdots\)
432.6.a.e 432.a 1.a $1$ $69.286$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(25\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+5^{2}q^{7}-427q^{13}+1711q^{19}-5^{5}q^{25}+\cdots\)
432.6.a.f 432.a 1.a $1$ $69.286$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(211\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+211q^{7}-775q^{13}-3143q^{19}+\cdots\)
432.6.a.g 432.a 1.a $1$ $69.286$ \(\Q\) None \(0\) \(0\) \(24\) \(-77\) $-$ $-$ $\mathrm{SU}(2)$ \(q+24q^{5}-77q^{7}-408q^{11}+89q^{13}+\cdots\)
432.6.a.h 432.a 1.a $1$ $69.286$ \(\Q\) None \(0\) \(0\) \(29\) \(-201\) $+$ $+$ $\mathrm{SU}(2)$ \(q+29q^{5}-201q^{7}+43q^{11}+244q^{13}+\cdots\)
432.6.a.i 432.a 1.a $1$ $69.286$ \(\Q\) None \(0\) \(0\) \(33\) \(-59\) $-$ $-$ $\mathrm{SU}(2)$ \(q+33q^{5}-59q^{7}-147q^{11}+836q^{13}+\cdots\)
432.6.a.j 432.a 1.a $1$ $69.286$ \(\Q\) None \(0\) \(0\) \(84\) \(193\) $-$ $+$ $\mathrm{SU}(2)$ \(q+84q^{5}+193q^{7}-348q^{11}+845q^{13}+\cdots\)
432.6.a.k 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-72\) \(8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-6^{2}-5\beta )q^{5}+(4-9\beta )q^{7}+(261+\cdots)q^{11}+\cdots\)
432.6.a.l 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{185}) \) None \(0\) \(0\) \(-38\) \(294\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-19-\beta )q^{5}+(147-\beta )q^{7}+(-65+\cdots)q^{11}+\cdots\)
432.6.a.m 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{85}) \) None \(0\) \(0\) \(-28\) \(-54\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-14-\beta )q^{5}+(-3^{3}-2\beta )q^{7}+(74+\cdots)q^{11}+\cdots\)
432.6.a.n 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{209}) \) None \(0\) \(0\) \(-20\) \(-12\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-10-\beta )q^{5}+(-6-\beta )q^{7}+(-119+\cdots)q^{11}+\cdots\)
432.6.a.o 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(-334\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-167q^{7}+13\beta q^{11}-235q^{13}+\cdots\)
432.6.a.p 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(-58\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-29q^{7}-\beta q^{11}+329q^{13}+\cdots\)
432.6.a.q 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{41}) \) None \(0\) \(0\) \(0\) \(32\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+(2^{4}+3\beta )q^{7}+(-3^{5}-8\beta )q^{11}+\cdots\)
432.6.a.r 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{41}) \) None \(0\) \(0\) \(0\) \(32\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+(2^{4}-3\beta )q^{7}+(3^{5}-8\beta )q^{11}+\cdots\)
432.6.a.s 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{209}) \) None \(0\) \(0\) \(20\) \(-12\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(10+\beta )q^{5}+(-6-\beta )q^{7}+(119+12\beta )q^{11}+\cdots\)
432.6.a.t 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{85}) \) None \(0\) \(0\) \(28\) \(-54\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(14+\beta )q^{5}+(-3^{3}-2\beta )q^{7}+(-74+\cdots)q^{11}+\cdots\)
432.6.a.u 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{185}) \) None \(0\) \(0\) \(38\) \(294\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(19+\beta )q^{5}+(147-\beta )q^{7}+(65-6\beta )q^{11}+\cdots\)
432.6.a.v 432.a 1.a $2$ $69.286$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(72\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(6^{2}+5\beta )q^{5}+(4-9\beta )q^{7}+(-261+\cdots)q^{11}+\cdots\)
432.6.a.w 432.a 1.a $3$ $69.286$ 3.3.2292.1 None \(0\) \(0\) \(-36\) \(-15\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-12-\beta _{1})q^{5}+(-5+\beta _{1}-\beta _{2})q^{7}+\cdots\)
432.6.a.x 432.a 1.a $3$ $69.286$ 3.3.2292.1 None \(0\) \(0\) \(36\) \(-15\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(12+\beta _{1})q^{5}+(-5+\beta _{1}-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(432))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(432)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 2}\)