Properties

Label 384.10.o
Level $384$
Weight $10$
Character orbit 384.o
Rep. character $\chi_{384}(47,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $568$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 384.o (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(384, [\chi])\).

Total New Old
Modular forms 2336 584 1752
Cusp forms 2272 568 1704
Eisenstein series 64 16 48

Trace form

\( 568 q + 4 q^{3} + 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 568 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 8 q^{19} - 4 q^{21} - 8 q^{25} - 12650084 q^{27} - 8 q^{33} - 8 q^{37} + 72274204 q^{39} + 8 q^{43} - 4 q^{45} + 78736 q^{51} - 140108824 q^{55} - 4 q^{57} - 180242216 q^{61} + 805675976 q^{67} - 4 q^{69} - 8 q^{73} - 7812496 q^{75} + 2269128688 q^{79} - 15625008 q^{85} + 2350951628 q^{87} + 1091566808 q^{91} + 78728 q^{93} - 16 q^{97} + 1556825028 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)