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Properties

Label 384.2.j
Level $384$
Weight $2$
Character orbit 384.j
Rep. character $\chi_{384}(97,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $2$
Sturm bound $128$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(384, [\chi])\).

Total New Old
Modular forms 160 16 144
Cusp forms 96 16 80
Eisenstein series 64 0 64

Trace form

\( 16 q + O(q^{10}) \) \( 16 q + 32 q^{29} + 32 q^{37} - 16 q^{49} - 32 q^{53} - 32 q^{61} - 32 q^{65} - 32 q^{69} - 32 q^{77} - 16 q^{81} + 32 q^{85} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.2.j.a 384.j 16.e $8$ $3.066$ 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(\beta _{3}-\beta _{5})q^{5}+(\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
384.2.j.b 384.j 16.e $8$ $3.066$ 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}+(-\beta _{2}+\beta _{6})q^{5}+(\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

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