Properties

Label 384.7.h
Level $384$
Weight $7$
Character orbit 384.h
Rep. character $\chi_{384}(65,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $8$
Sturm bound $448$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(448\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(384, [\chi])\).

Total New Old
Modular forms 400 96 304
Cusp forms 368 96 272
Eisenstein series 32 0 32

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 300000 q^{25} + 88160 q^{33} + 1201632 q^{49} - 488480 q^{57} + 1028160 q^{73} - 2388512 q^{81} + 2505216 q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.7.h.a 384.h 24.h $2$ $88.341$ \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-6}) \) \(0\) \(-54\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{3}q^{3}+7\beta q^{5}-17\beta q^{7}+3^{6}q^{9}+\cdots\)
384.7.h.b 384.h 24.h $2$ $88.341$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-46\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-23+\beta )q^{3}+(329-46\beta )q^{9}-2338q^{11}+\cdots\)
384.7.h.c 384.h 24.h $2$ $88.341$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(46\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(23-\beta )q^{3}+(329-46\beta )q^{9}+2338q^{11}+\cdots\)
384.7.h.d 384.h 24.h $2$ $88.341$ \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-6}) \) \(0\) \(54\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3^{3}q^{3}+7\beta q^{5}+17\beta q^{7}+3^{6}q^{9}+\cdots\)
384.7.h.e 384.h 24.h $8$ $88.341$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-72\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-9+\beta _{5})q^{3}-\beta _{6}q^{5}+(\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots\)
384.7.h.f 384.h 24.h $8$ $88.341$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(72\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(9-\beta _{4})q^{3}-\beta _{6}q^{5}+(-\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots\)
384.7.h.g 384.h 24.h $24$ $88.341$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
384.7.h.h 384.h 24.h $48$ $88.341$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)