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Properties

Label 864.4.f
Level $864$
Weight $4$
Character orbit 864.f
Rep. character $\chi_{864}(431,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $2$
Sturm bound $576$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 864.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(864, [\chi])\).

Total New Old
Modular forms 456 48 408
Cusp forms 408 48 360
Eisenstein series 48 0 48

Trace form

\( 48 q + O(q^{10}) \) \( 48 q + 24 q^{19} + 1200 q^{25} - 432 q^{43} - 2712 q^{49} - 3264 q^{67} + 216 q^{73} - 1800 q^{91} - 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.4.f.a 864.f 24.f $24$ $50.978$ None 216.4.f.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
864.4.f.b 864.f 24.f $24$ $50.978$ None 216.4.f.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(864, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)