Properties

Label 216.4.a
Level $216$
Weight $4$
Character orbit 216.a
Rep. character $\chi_{216}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $8$
Sturm bound $144$
Trace bound $5$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 216.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(216))\).

Total New Old
Modular forms 120 12 108
Cusp forms 96 12 84
Eisenstein series 24 0 24

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.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(5\)

Trace form

\( 12q + 24q^{7} + O(q^{10}) \) \( 12q + 24q^{7} + 6q^{13} + 90q^{19} + 522q^{25} + 210q^{31} + 894q^{37} - 180q^{43} + 744q^{49} - 1746q^{55} - 486q^{61} + 714q^{67} + 2748q^{73} - 714q^{79} - 4704q^{85} - 6294q^{91} - 936q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(216))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
216.4.a.a \(1\) \(12.744\) \(\Q\) None \(0\) \(0\) \(-4\) \(3\) \(-\) \(+\) \(q-4q^{5}+3q^{7}-28q^{11}-11q^{13}+\cdots\)
216.4.a.b \(1\) \(12.744\) \(\Q\) None \(0\) \(0\) \(-1\) \(-9\) \(-\) \(+\) \(q-q^{5}-9q^{7}+17q^{11}-44q^{13}-56q^{17}+\cdots\)
216.4.a.c \(1\) \(12.744\) \(\Q\) None \(0\) \(0\) \(1\) \(-9\) \(+\) \(-\) \(q+q^{5}-9q^{7}-17q^{11}-44q^{13}+56q^{17}+\cdots\)
216.4.a.d \(1\) \(12.744\) \(\Q\) None \(0\) \(0\) \(4\) \(3\) \(+\) \(+\) \(q+4q^{5}+3q^{7}+28q^{11}-11q^{13}+\cdots\)
216.4.a.e \(2\) \(12.744\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-8\) \(24\) \(-\) \(-\) \(q+(-4-\beta )q^{5}+(12+\beta )q^{7}-q^{11}+\cdots\)
216.4.a.f \(2\) \(12.744\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-4\) \(-6\) \(+\) \(-\) \(q+(-2-\beta )q^{5}+(-3+2\beta )q^{7}+(-26+\cdots)q^{11}+\cdots\)
216.4.a.g \(2\) \(12.744\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(4\) \(-6\) \(-\) \(-\) \(q+(2+\beta )q^{5}+(-3+2\beta )q^{7}+(26-3\beta )q^{11}+\cdots\)
216.4.a.h \(2\) \(12.744\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(8\) \(24\) \(+\) \(+\) \(q+(4+\beta )q^{5}+(12+\beta )q^{7}+q^{11}+(2^{4}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(216))\) into lower level spaces

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