Properties

Label 1344.4.by
Level $1344$
Weight $4$
Character orbit 1344.by
Rep. character $\chi_{1344}(529,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $384$
Sturm bound $1024$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1344.by (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1344, [\chi])\).

Total New Old
Modular forms 3136 384 2752
Cusp forms 3008 384 2624
Eisenstein series 128 0 128

Trace form

\( 384q + O(q^{10}) \) \( 384q - 40q^{11} + 800q^{29} - 1488q^{31} - 456q^{35} - 16q^{37} - 1616q^{43} - 752q^{53} + 1376q^{59} + 1440q^{67} + 15552q^{81} - 3496q^{91} + 7728q^{95} + 720q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)