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Properties

Label 384.3.g
Level $384$
Weight $3$
Character orbit 384.g
Rep. character $\chi_{384}(127,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 144 16 128
Cusp forms 112 16 96
Eisenstein series 32 0 32

Trace form

\( 16 q - 48 q^{9} + O(q^{10}) \) \( 16 q - 48 q^{9} + 32 q^{17} - 16 q^{25} + 160 q^{41} - 176 q^{49} + 192 q^{57} - 320 q^{65} - 32 q^{73} + 144 q^{81} - 480 q^{89} + 800 q^{97} + O(q^{100}) \)

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.g.a 384.g 4.b $8$ $10.463$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}q^{3}+(-2+\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
384.3.g.b 384.g 4.b $8$ $10.463$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}q^{3}+(2-\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)