Properties

Label 432.4.a
Level $432$
Weight $4$
Character orbit 432.a
Rep. character $\chi_{432}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $19$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 432.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(432))\).

Total New Old
Modular forms 234 24 210
Cusp forms 198 24 174
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
\(+\)\(+\)$+$\(7\)
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(6\)
\(-\)\(-\)$+$\(6\)
Plus space\(+\)\(13\)
Minus space\(-\)\(11\)

Trace form

\( 24 q - 18 q^{7} + O(q^{10}) \) \( 24 q - 18 q^{7} - 102 q^{19} + 516 q^{25} - 108 q^{31} + 528 q^{37} + 120 q^{43} + 1560 q^{49} + 540 q^{55} - 168 q^{61} + 1290 q^{67} + 384 q^{73} + 2070 q^{79} - 2544 q^{85} + 2118 q^{91} - 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(432))\) 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
432.4.a.a 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(-15\) \(25\) $-$ $+$ $\mathrm{SU}(2)$ \(q-15q^{5}+5^{2}q^{7}-15q^{11}+20q^{13}+\cdots\)
432.4.a.b 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(-12\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q-12q^{5}+7q^{7}+60q^{11}-79q^{13}+\cdots\)
432.4.a.c 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(-9\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-9q^{5}+q^{7}+63q^{11}-28q^{13}-72q^{17}+\cdots\)
432.4.a.d 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(-4\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-3q^{7}+28q^{11}-11q^{13}+\cdots\)
432.4.a.e 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(-3\) \(-29\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-29q^{7}-57q^{11}+20q^{13}+\cdots\)
432.4.a.f 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(-1\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+9q^{7}-17q^{11}-44q^{13}-56q^{17}+\cdots\)
432.4.a.g 432.a 1.a $1$ $25.489$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-17\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-17q^{7}+89q^{13}-107q^{19}-5^{3}q^{25}+\cdots\)
432.4.a.h 432.a 1.a $1$ $25.489$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(37\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+37q^{7}-19q^{13}+163q^{19}-5^{3}q^{25}+\cdots\)
432.4.a.i 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(1\) \(9\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+9q^{7}+17q^{11}-44q^{13}+56q^{17}+\cdots\)
432.4.a.j 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(3\) \(-29\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-29q^{7}+57q^{11}+20q^{13}+\cdots\)
432.4.a.k 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(4\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-3q^{7}-28q^{11}-11q^{13}+\cdots\)
432.4.a.l 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(9\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+9q^{5}+q^{7}-63q^{11}-28q^{13}+72q^{17}+\cdots\)
432.4.a.m 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(12\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q+12q^{5}+7q^{7}-60q^{11}-79q^{13}+\cdots\)
432.4.a.n 432.a 1.a $1$ $25.489$ \(\Q\) None \(0\) \(0\) \(15\) \(25\) $-$ $-$ $\mathrm{SU}(2)$ \(q+15q^{5}+5^{2}q^{7}+15q^{11}+20q^{13}+\cdots\)
432.4.a.o 432.a 1.a $2$ $25.489$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-8\) \(-24\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-4-\beta )q^{5}+(-12-\beta )q^{7}+q^{11}+\cdots\)
432.4.a.p 432.a 1.a $2$ $25.489$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-4\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{5}+(3-2\beta )q^{7}+(26-3\beta )q^{11}+\cdots\)
432.4.a.q 432.a 1.a $2$ $25.489$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-22\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-11q^{7}+\beta q^{11}+29q^{13}+\cdots\)
432.4.a.r 432.a 1.a $2$ $25.489$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(4\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(3-2\beta )q^{7}+(-26+3\beta )q^{11}+\cdots\)
432.4.a.s 432.a 1.a $2$ $25.489$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(8\) \(-24\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(4+\beta )q^{5}+(-12-\beta )q^{7}-q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(432))\) into lower level spaces

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