Properties

Label 384.3.e
Level $384$
Weight $3$
Character orbit 384.e
Rep. character $\chi_{384}(257,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $4$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

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

Total New Old
Modular forms 144 32 112
Cusp forms 112 32 80
Eisenstein series 32 0 32

Trace form

\( 32q + O(q^{10}) \) \( 32q - 160q^{25} + 32q^{33} + 288q^{49} - 160q^{57} - 320q^{73} + 288q^{81} + 384q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
384.3.e.a \(8\) \(10.463\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-4\) \(0\) \(-8\) \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(-1-\beta _{2})q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
384.3.e.b \(8\) \(10.463\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-4\) \(0\) \(8\) \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{3})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
384.3.e.c \(8\) \(10.463\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(4\) \(0\) \(-8\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-1-\beta _{3})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
384.3.e.d \(8\) \(10.463\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(4\) \(0\) \(8\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{2})q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)

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

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