Properties

Label 384.3.h
Level $384$
Weight $3$
Character orbit 384.h
Rep. character $\chi_{384}(65,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $7$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

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

\( 32q + O(q^{10}) \) \( 32q + 160q^{25} + 32q^{33} + 160q^{49} + 160q^{57} - 320q^{73} + 160q^{81} - 512q^{97} + O(q^{100}) \)

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.h.a \(2\) \(10.463\) \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-6}) \) \(0\) \(-6\) \(0\) \(0\) \(q-3q^{3}+\beta q^{5}+\beta q^{7}+9q^{9}-10q^{11}+\cdots\)
384.3.h.b \(2\) \(10.463\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta )q^{3}+(-7-2\beta )q^{9}-14q^{11}+\cdots\)
384.3.h.c \(2\) \(10.463\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+(-7+2\beta )q^{9}+14q^{11}+\cdots\)
384.3.h.d \(2\) \(10.463\) \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-6}) \) \(0\) \(6\) \(0\) \(0\) \(q+3q^{3}+\beta q^{5}-\beta q^{7}+9q^{9}+10q^{11}+\cdots\)
384.3.h.e \(4\) \(10.463\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(-16\) \(0\) \(q+\beta _{3}q^{3}-4q^{5}+(-2\beta _{1}-2\beta _{3})q^{7}+\cdots\)
384.3.h.f \(4\) \(10.463\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(16\) \(0\) \(q-\beta _{1}q^{3}+4q^{5}+(-2\beta _{1}-2\beta _{3})q^{7}+\cdots\)
384.3.h.g \(16\) \(10.463\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots\)

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

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