Properties

Label 864.2.y
Level 864
Weight 2
Character orbit y
Rep. character \(\chi_{864}(97,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 216
Newform subspaces 4
Sturm bound 288
Trace bound 11

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Defining parameters

Level: \( N \) = \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 864.y (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).

Total New Old
Modular forms 912 216 696
Cusp forms 816 216 600
Eisenstein series 96 0 96

Trace form

\( 216q + O(q^{10}) \) \( 216q + 24q^{29} - 36q^{33} - 36q^{41} + 24q^{45} + 12q^{57} + 48q^{65} + 48q^{69} + 48q^{77} + 48q^{81} - 12q^{89} + 144q^{93} + 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
864.2.y.a \(48\) \(6.899\) None \(0\) \(0\) \(0\) \(0\)
864.2.y.b \(54\) \(6.899\) None \(0\) \(0\) \(0\) \(0\)
864.2.y.c \(54\) \(6.899\) None \(0\) \(0\) \(0\) \(0\)
864.2.y.d \(60\) \(6.899\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database