Properties

Label 384.5.l
Level $384$
Weight $5$
Character orbit 384.l
Rep. character $\chi_{384}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $2$
Sturm bound $320$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 384.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(320\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(384, [\chi])\).

Total New Old
Modular forms 544 64 480
Cusp forms 480 64 416
Eisenstein series 64 0 64

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 3456 q^{29} - 7296 q^{37} + 21952 q^{49} - 1920 q^{53} - 7552 q^{61} + 8064 q^{65} + 19584 q^{69} - 18816 q^{77} - 46656 q^{81} + 22400 q^{85} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.5.l.a 384.l 16.f $32$ $39.694$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
384.5.l.b 384.l 16.f $32$ $39.694$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)