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Properties

Label 384.9.p
Level $384$
Weight $9$
Character orbit 384.p
Rep. character $\chi_{384}(17,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $504$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 384.p (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(384, [\chi])\).

Total New Old
Modular forms 2080 520 1560
Cusp forms 2016 504 1512
Eisenstein series 64 16 48

Trace form

\( 504 q + 4 q^{3} + 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 504 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{19} - 4 q^{21} - 8 q^{25} - 51068 q^{27} + 16 q^{31} - 8 q^{33} - 8 q^{37} + 7650052 q^{39} + 8 q^{43} - 4 q^{45} + 26248 q^{51} + 46326792 q^{55} - 4 q^{57} - 48952072 q^{61} + 8 q^{63} + 149408776 q^{67} - 4 q^{69} - 8 q^{73} + 1562504 q^{75} - 3125008 q^{85} + 149712644 q^{87} - 350400760 q^{91} - 26248 q^{93} - 16 q^{97} + 630017028 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

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

Decomposition of \(S_{9}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)