Properties

Label 432.2.a
Level $432$
Weight $2$
Character orbit 432.a
Rep. character $\chi_{432}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $8$
Sturm bound $144$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(432))\).

Total New Old
Modular forms 90 8 82
Cusp forms 55 8 47
Eisenstein series 35 0 35

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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(5\)

Trace form

\( 8q - 2q^{7} + O(q^{10}) \) \( 8q - 2q^{7} + 2q^{19} + 12q^{25} + 20q^{31} - 16q^{37} + 24q^{43} + 8q^{49} - 4q^{55} - 24q^{61} - 46q^{67} - 42q^{79} - 16q^{85} + 14q^{91} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(432))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
432.2.a.a \(1\) \(3.450\) \(\Q\) None \(0\) \(0\) \(-4\) \(3\) \(+\) \(-\) \(q-4q^{5}+3q^{7}+4q^{11}+q^{13}+4q^{17}+\cdots\)
432.2.a.b \(1\) \(3.450\) \(\Q\) None \(0\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(q-3q^{5}+q^{7}-3q^{11}-4q^{13}-2q^{19}+\cdots\)
432.2.a.c \(1\) \(3.450\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(+\) \(+\) \(q-q^{5}-3q^{7}-5q^{11}+4q^{13}-8q^{17}+\cdots\)
432.2.a.d \(1\) \(3.450\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(-\) \(-\) \(q-5q^{7}-7q^{13}+q^{19}-5q^{25}+4q^{31}+\cdots\)
432.2.a.e \(1\) \(3.450\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(q+q^{7}+5q^{13}+7q^{19}-5q^{25}+4q^{31}+\cdots\)
432.2.a.f \(1\) \(3.450\) \(\Q\) None \(0\) \(0\) \(1\) \(-3\) \(+\) \(-\) \(q+q^{5}-3q^{7}+5q^{11}+4q^{13}+8q^{17}+\cdots\)
432.2.a.g \(1\) \(3.450\) \(\Q\) None \(0\) \(0\) \(3\) \(1\) \(-\) \(+\) \(q+3q^{5}+q^{7}+3q^{11}-4q^{13}-2q^{19}+\cdots\)
432.2.a.h \(1\) \(3.450\) \(\Q\) None \(0\) \(0\) \(4\) \(3\) \(+\) \(-\) \(q+4q^{5}+3q^{7}-4q^{11}+q^{13}-4q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(432))\) into lower level spaces

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