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Properties

Label 1344.4.cc
Level $1344$
Weight $4$
Character orbit 1344.cc
Rep. character $\chi_{1344}(431,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $752$
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.cc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
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 784 2352
Cusp forms 3008 752 2256
Eisenstein series 128 32 96

Trace form

\( 752 q + 2 q^{3} + 16 q^{7} + O(q^{10}) \) \( 752 q + 2 q^{3} + 16 q^{7} - 16 q^{13} + 4 q^{19} + 50 q^{21} + 8 q^{27} - 4 q^{33} - 4 q^{37} + 4 q^{39} + 16 q^{43} + 498 q^{45} - 16 q^{49} + 810 q^{51} + 32 q^{55} - 4 q^{61} - 1628 q^{67} - 116 q^{69} + 360 q^{75} - 4 q^{81} - 1016 q^{85} + 4 q^{87} + 4552 q^{91} - 110 q^{93} - 32 q^{97} - 2908 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)