Properties

Label 216.2.a
Level $216$
Weight $2$
Character orbit 216.a
Rep. character $\chi_{216}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(216))\).

Total New Old
Modular forms 48 4 44
Cusp forms 25 4 21
Eisenstein series 23 0 23

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

Trace form

\( 4 q + O(q^{10}) \) \( 4 q + 10 q^{13} + 2 q^{19} + 14 q^{25} - 22 q^{31} - 30 q^{37} - 20 q^{43} + 8 q^{49} + 22 q^{55} - 26 q^{61} + 2 q^{67} + 4 q^{73} + 22 q^{79} - 16 q^{85} + 18 q^{91} + 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(216))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
216.2.a.a \(1\) \(1.725\) \(\Q\) None \(0\) \(0\) \(-4\) \(-3\) \(+\) \(+\) \(q-4q^{5}-3q^{7}-4q^{11}+q^{13}+4q^{17}+\cdots\)
216.2.a.b \(1\) \(1.725\) \(\Q\) None \(0\) \(0\) \(-1\) \(3\) \(+\) \(-\) \(q-q^{5}+3q^{7}+5q^{11}+4q^{13}-8q^{17}+\cdots\)
216.2.a.c \(1\) \(1.725\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(-\) \(+\) \(q+q^{5}+3q^{7}-5q^{11}+4q^{13}+8q^{17}+\cdots\)
216.2.a.d \(1\) \(1.725\) \(\Q\) None \(0\) \(0\) \(4\) \(-3\) \(-\) \(+\) \(q+4q^{5}-3q^{7}+4q^{11}+q^{13}-4q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(216))\) into lower level spaces

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