↑

Properties

Label 1344.4.cg
Level $1344$
Weight $4$
Character orbit 1344.cg
Rep. character $\chi_{1344}(85,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2304$
Sturm bound $1024$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1344.cg (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1024\)

Dimensions

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

Total New Old
Modular forms 6176 2304 3872
Cusp forms 6112 2304 3808
Eisenstein series 64 0 64

Trace form

\( 2304 q + O(q^{10}) \) \( 2304 q + 944 q^{22} - 160 q^{26} - 4960 q^{32} - 4000 q^{34} + 6560 q^{40} + 2000 q^{44} + 5952 q^{51} - 864 q^{54} + 1152 q^{55} + 784 q^{56} + 4896 q^{60} + 11712 q^{62} - 2016 q^{63} - 1632 q^{67} + 8256 q^{68} + 2016 q^{70} - 5264 q^{74} + 8832 q^{75} - 2976 q^{76} + 11328 q^{79} - 6240 q^{88} - 17856 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)