Properties

Label 384.5.h
Level $384$
Weight $5$
Character orbit 384.h
Rep. character $\chi_{384}(65,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $8$
Sturm bound $320$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 384.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(320\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(384, [\chi])\).

Total New Old
Modular forms 272 64 208
Cusp forms 240 64 176
Eisenstein series 32 0 32

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 8000 q^{25} - 1984 q^{33} + 27968 q^{49} - 2240 q^{57} + 14720 q^{73} + 17728 q^{81} + 11264 q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.5.h.a 384.h 24.h $2$ $39.694$ \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-6}) \) \(0\) \(-18\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-9q^{3}+\beta q^{5}-5\beta q^{7}+3^{4}q^{9}-142q^{11}+\cdots\)
384.5.h.b 384.h 24.h $2$ $39.694$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-14\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-7-\beta )q^{3}+(17+14\beta )q^{9}+46q^{11}+\cdots\)
384.5.h.c 384.h 24.h $2$ $39.694$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(14\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(7+\beta )q^{3}+(17+14\beta )q^{9}-46q^{11}+\cdots\)
384.5.h.d 384.h 24.h $2$ $39.694$ \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-6}) \) \(0\) \(18\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+9q^{3}+\beta q^{5}+5\beta q^{7}+3^{4}q^{9}+142q^{11}+\cdots\)
384.5.h.e 384.h 24.h $4$ $39.694$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3-\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+(-63+\cdots)q^{9}+\cdots\)
384.5.h.f 384.h 24.h $4$ $39.694$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3-\beta _{1})q^{3}-\beta _{2}q^{5}+\beta _{2}q^{7}+(-63+\cdots)q^{9}+\cdots\)
384.5.h.g 384.h 24.h $16$ $39.694$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+\beta _{8}q^{5}+\beta _{7}q^{7}+(-7-\beta _{5}+\cdots)q^{9}+\cdots\)
384.5.h.h 384.h 24.h $32$ $39.694$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

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