↑

Properties

Label 1224.4.bs
Level $1224$
Weight $4$
Character orbit 1224.bs
Rep. character $\chi_{1224}(253,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1072$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 2624 1088 1536
Cusp forms 2560 1072 1488
Eisenstein series 64 16 48

Trace form

\( 1072 q + 4 q^{2} - 8 q^{7} + 4 q^{8} + O(q^{10}) \) \( 1072 q + 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{10} - 204 q^{14} - 8 q^{16} + 8 q^{17} + 260 q^{20} + 500 q^{22} + 8 q^{23} + 80 q^{25} + 404 q^{26} + 180 q^{28} - 8 q^{31} + 764 q^{32} - 532 q^{34} + 1152 q^{40} + 480 q^{41} - 972 q^{44} - 940 q^{46} - 8 q^{49} + 1248 q^{50} - 520 q^{52} - 236 q^{56} + 352 q^{58} - 2212 q^{62} + 3448 q^{65} - 1180 q^{68} + 512 q^{70} - 440 q^{71} - 1488 q^{73} + 3044 q^{74} - 1560 q^{76} - 8 q^{79} + 632 q^{80} - 1032 q^{82} + 12064 q^{86} - 2904 q^{88} + 2084 q^{92} + 3672 q^{94} + 8 q^{95} - 8 q^{97} + O(q^{100}) \)

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

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