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Properties

Label 1224.4.cj
Level $1224$
Weight $4$
Character orbit 1224.cj
Rep. character $\chi_{1224}(91,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2144$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1224.cj (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1224, [\chi])\).

Total New Old
Modular forms 5248 2176 3072
Cusp forms 5120 2144 2976
Eisenstein series 128 32 96

Trace form

\( 2144 q + 8 q^{2} - 8 q^{4} + 8 q^{8} + O(q^{10}) \) \( 2144 q + 8 q^{2} - 8 q^{4} + 8 q^{8} - 8 q^{10} + 16 q^{11} + 8 q^{14} + 16 q^{17} - 16 q^{19} + 8 q^{20} - 8 q^{22} - 16 q^{25} - 728 q^{26} + 136 q^{28} - 1232 q^{32} + 1048 q^{34} + 32 q^{35} + 528 q^{38} - 584 q^{40} + 16 q^{41} - 16 q^{43} + 2472 q^{44} + 1960 q^{46} - 16 q^{49} - 16 q^{52} + 2608 q^{56} + 1280 q^{58} + 16 q^{59} - 2064 q^{62} - 2648 q^{64} - 4864 q^{65} - 5888 q^{68} - 5440 q^{70} + 2944 q^{73} - 1192 q^{74} + 272 q^{76} + 5992 q^{80} + 5712 q^{82} + 16 q^{83} - 11104 q^{86} + 5176 q^{88} + 16 q^{89} - 16 q^{91} - 1224 q^{92} + 4312 q^{94} - 16 q^{97} + 12112 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)