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Properties

Label 1224.4.j
Level $1224$
Weight $4$
Character orbit 1224.j
Rep. character $\chi_{1224}(35,\cdot)$
Character field $\Q$
Dimension $192$
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.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
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 656 192 464
Cusp forms 640 192 448
Eisenstein series 16 0 16

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 144 q^{10} + 24 q^{16} + 408 q^{22} + 4800 q^{25} + 168 q^{28} - 2856 q^{40} + 1728 q^{43} + 1440 q^{46} - 10848 q^{49} + 1752 q^{52} - 3624 q^{58} - 3384 q^{64} - 1632 q^{67} + 3768 q^{70} + 864 q^{73} + 3576 q^{76} - 8280 q^{82} - 3024 q^{88} + 1752 q^{94} - 192 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)