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Properties

Label 384.3.m
Level $384$
Weight $3$
Character orbit 384.m
Rep. character $\chi_{384}(79,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $64$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.m (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(384, [\chi])\).

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

Trace form

\( 64 q + O(q^{10}) \) \( 64 q - 128 q^{23} + 192 q^{35} + 192 q^{43} + 192 q^{51} + 320 q^{53} + 256 q^{55} + 256 q^{59} + 64 q^{61} - 64 q^{67} - 192 q^{69} - 512 q^{71} - 384 q^{75} - 448 q^{77} - 512 q^{79} - 192 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.3.m.a 384.m 32.h $64$ $10.463$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{3}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)