Properties

Label 384.7.e
Level $384$
Weight $7$
Character orbit 384.e
Rep. character $\chi_{384}(257,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $4$
Sturm bound $448$
Trace bound $7$

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Defining parameters

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

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

\( 96 q + O(q^{10}) \) \( 96 q - 300000 q^{25} + 88160 q^{33} + 2025312 q^{49} + 488480 q^{57} + 1028160 q^{73} - 32928 q^{81} - 5921664 q^{97} + O(q^{100}) \)

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.e.a 384.e 3.b $24$ $88.341$ None \(0\) \(-20\) \(0\) \(-408\) $\mathrm{SU}(2)[C_{2}]$
384.7.e.b 384.e 3.b $24$ $88.341$ None \(0\) \(-20\) \(0\) \(408\) $\mathrm{SU}(2)[C_{2}]$
384.7.e.c 384.e 3.b $24$ $88.341$ None \(0\) \(20\) \(0\) \(-408\) $\mathrm{SU}(2)[C_{2}]$
384.7.e.d 384.e 3.b $24$ $88.341$ None \(0\) \(20\) \(0\) \(408\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{7}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)