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Properties

Label 864.1.t
Level $864$
Weight $1$
Character orbit 864.t
Rep. character $\chi_{864}(559,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 864.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(864, [\chi])\).

Total New Old
Modular forms 72 6 66
Cusp forms 24 2 22
Eisenstein series 48 4 44

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + O(q^{10}) \) \( 2 q + q^{11} + 2 q^{17} + 2 q^{19} - q^{25} - q^{41} - q^{43} - q^{49} + q^{59} - q^{67} - 2 q^{73} - 2 q^{83} - 4 q^{89} + q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.1.t.a 864.t 72.p $2$ $0.431$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{11}+q^{17}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)