Properties

Label 384.2.v
Level $384$
Weight $2$
Character orbit 384.v
Rep. character $\chi_{384}(13,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $512$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.v (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 128 \)
Character field: \(\Q(\zeta_{32})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 1056 512 544
Cusp forms 992 512 480
Eisenstein series 64 0 64

Trace form

\( 512 q + O(q^{10}) \) \( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.2.v.a $512$ $3.066$ None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)