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Properties

Label 1224.4.f
Level $1224$
Weight $4$
Character orbit 1224.f
Rep. character $\chi_{1224}(613,\cdot)$
Character field $\Q$
Dimension $240$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 656 240 416
Cusp forms 640 240 400
Eisenstein series 16 0 16

Trace form

\( 240 q + 2 q^{2} + 10 q^{4} + 28 q^{7} - 70 q^{8} + O(q^{10}) \) \( 240 q + 2 q^{2} + 10 q^{4} + 28 q^{7} - 70 q^{8} - 78 q^{10} + 4 q^{14} + 42 q^{16} + 170 q^{20} + 26 q^{22} + 52 q^{23} - 6000 q^{25} + 592 q^{26} - 360 q^{28} - 372 q^{31} - 238 q^{32} - 1680 q^{38} + 1838 q^{40} + 2214 q^{44} - 52 q^{46} - 408 q^{47} + 11040 q^{49} + 2266 q^{50} - 852 q^{52} - 288 q^{55} - 1356 q^{56} - 2074 q^{58} - 2700 q^{62} + 754 q^{64} + 768 q^{70} - 3468 q^{71} - 432 q^{73} + 3706 q^{74} - 4692 q^{76} - 1460 q^{79} - 3622 q^{80} + 1956 q^{82} - 7276 q^{86} + 1846 q^{88} + 848 q^{89} + 3180 q^{92} + 1400 q^{94} + 8144 q^{95} + 3072 q^{97} + 4554 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1224, [\chi]) \cong \)