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Properties

Label 384.3.p
Level $384$
Weight $3$
Character orbit 384.p
Rep. character $\chi_{384}(17,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $120$
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.p (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
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 544 136 408
Cusp forms 480 120 360
Eisenstein series 64 16 48

Trace form

\( 120 q + 4 q^{3} + 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 120 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{19} - 4 q^{21} - 8 q^{25} - 92 q^{27} + 16 q^{31} - 8 q^{33} - 8 q^{37} + 196 q^{39} + 8 q^{43} - 4 q^{45} + 40 q^{51} + 264 q^{55} - 4 q^{57} + 56 q^{61} + 8 q^{63} - 248 q^{67} - 4 q^{69} - 8 q^{73} + 104 q^{75} - 208 q^{85} + 452 q^{87} + 200 q^{91} - 40 q^{93} - 16 q^{97} - 252 q^{99} + O(q^{100}) \)

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.p.a 384.p 96.p $120$ $10.463$ None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{8}]$

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

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