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Properties

Label 1224.4.t
Level $1224$
Weight $4$
Character orbit 1224.t
Rep. character $\chi_{1224}(829,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $536$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1312 544 768
Cusp forms 1280 536 744
Eisenstein series 32 8 24

Trace form

\( 536 q - 4 q^{4} - 4 q^{7} + O(q^{10}) \) \( 536 q - 4 q^{4} - 4 q^{7} - 78 q^{10} + 40 q^{14} - 268 q^{16} + 56 q^{17} - 86 q^{20} - 270 q^{22} + 4 q^{23} - 788 q^{28} + 524 q^{31} - 626 q^{34} - 224 q^{38} - 422 q^{40} - 272 q^{41} - 1058 q^{44} + 568 q^{46} + 1888 q^{47} - 620 q^{50} - 1404 q^{52} + 1752 q^{55} - 168 q^{56} - 1246 q^{58} - 2264 q^{62} + 188 q^{64} + 200 q^{65} - 446 q^{68} + 228 q^{71} - 744 q^{73} - 2230 q^{74} - 2836 q^{79} + 70 q^{80} + 1940 q^{82} - 1412 q^{86} - 2310 q^{88} + 8 q^{89} + 3080 q^{92} + 504 q^{95} - 912 q^{97} - 7184 q^{98} + O(q^{100}) \)

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

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