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Properties

Label 384.5.p
Level $384$
Weight $5$
Character orbit 384.p
Rep. character $\chi_{384}(17,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $248$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 384.p (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 1056 264 792
Cusp forms 992 248 744
Eisenstein series 64 16 48

Trace form

\( 248 q + 4 q^{3} + 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 248 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{19} - 4 q^{21} - 8 q^{25} + 3652 q^{27} + 16 q^{31} - 8 q^{33} - 8 q^{37} - 2684 q^{39} + 8 q^{43} - 4 q^{45} + 328 q^{51} - 11768 q^{55} - 4 q^{57} - 7560 q^{61} + 8 q^{63} + 30216 q^{67} - 4 q^{69} - 8 q^{73} + 2504 q^{75} - 5008 q^{85} - 49276 q^{87} - 31864 q^{91} - 328 q^{93} - 16 q^{97} + 46596 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

The newforms in this space have not yet been added to the LMFDB.

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

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