Properties

Label 384.10.c
Level $384$
Weight $10$
Character orbit 384.c
Rep. character $\chi_{384}(383,\cdot)$
Character field $\Q$
Dimension $144$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 384.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(640\)

Dimensions

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

Total New Old
Modular forms 592 144 448
Cusp forms 560 144 416
Eisenstein series 32 0 32

Trace form

\( 144 q + O(q^{10}) \) \( 144 q - 56250000 q^{25} - 75632 q^{33} - 778503024 q^{49} - 219408016 q^{57} - 887399712 q^{73} + 927683728 q^{81} - 4448121408 q^{97} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)