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Properties

Label 576.3.j
Level $576$
Weight $3$
Character orbit 576.j
Rep. character $\chi_{576}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

Total New Old
Modular forms 416 32 384
Cusp forms 352 32 320
Eisenstein series 64 0 64

Trace form

\( 32 q + O(q^{10}) \) \( 32 q - 64 q^{19} - 128 q^{43} - 224 q^{49} + 64 q^{61} + 64 q^{67} + 512 q^{79} + 320 q^{85} + 192 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.3.j.a 576.j 48.i $32$ $15.695$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)