Properties

Label 6561.2.a
Level $6561$
Weight $2$
Character orbit 6561.a
Rep. character $\chi_{6561}(1,\cdot)$
Character field $\Q$
Dimension $306$
Newform subspaces $5$
Sturm bound $1458$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 6561 = 3^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6561.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(1458\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6561))\).

Total New Old
Modular forms 783 342 441
Cusp forms 676 306 370
Eisenstein series 107 36 71

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)Dim
\(+\)\(144\)
\(-\)\(162\)

Trace form

\( 306 q + 288 q^{4} + O(q^{10}) \) \( 306 q + 288 q^{4} + 252 q^{16} + 234 q^{25} + 18 q^{28} + 198 q^{49} + 18 q^{55} + 36 q^{58} + 180 q^{64} - 36 q^{82} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6561))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3
6561.2.a.a 6561.a 1.a $36$ $52.390$ None \(-9\) \(0\) \(0\) \(-18\) $+$ $\mathrm{SU}(2)$
6561.2.a.b 6561.a 1.a $36$ $52.390$ None \(9\) \(0\) \(0\) \(-18\) $+$ $\mathrm{SU}(2)$
6561.2.a.c 6561.a 1.a $72$ $52.390$ None \(-9\) \(0\) \(-18\) \(0\) $+$ $\mathrm{SU}(2)$
6561.2.a.d 6561.a 1.a $72$ $52.390$ None \(9\) \(0\) \(18\) \(0\) $-$ $\mathrm{SU}(2)$
6561.2.a.e 6561.a 1.a $90$ $52.390$ None \(0\) \(0\) \(0\) \(36\) $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6561))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6561)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(729))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2187))\)\(^{\oplus 2}\)