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Properties

Label 384.8.o
Level $384$
Weight $8$
Character orbit 384.o
Rep. character $\chi_{384}(47,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $440$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 384.o (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(384, [\chi])\).

Total New Old
Modular forms 1824 456 1368
Cusp forms 1760 440 1320
Eisenstein series 64 16 48

Trace form

\( 440 q + 4 q^{3} + 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 440 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 8 q^{19} - 4 q^{21} - 8 q^{25} + 476092 q^{27} - 8 q^{33} - 8 q^{37} - 283940 q^{39} + 8 q^{43} - 4 q^{45} + 8752 q^{51} - 4191000 q^{55} - 4 q^{57} + 4559768 q^{61} - 3105080 q^{67} - 4 q^{69} - 8 q^{73} - 312496 q^{75} + 523760 q^{79} - 625008 q^{85} - 40789108 q^{87} + 3407000 q^{91} + 8744 q^{93} - 16 q^{97} + 9729732 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(384, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)