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Properties

Label 1323.4.s
Level $1323$
Weight $4$
Character orbit 1323.s
Rep. character $\chi_{1323}(656,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $232$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1323, [\chi])\).

Total New Old
Modular forms 1056 248 808
Cusp forms 960 232 728
Eisenstein series 96 16 80

Trace form

\( 232 q - 3 q^{2} + 447 q^{4} - 6 q^{5} + O(q^{10}) \) \( 232 q - 3 q^{2} + 447 q^{4} - 6 q^{5} + 6 q^{10} - 36 q^{13} - 1657 q^{16} + 72 q^{17} + 6 q^{19} - 24 q^{20} - 20 q^{22} + 5002 q^{25} + 96 q^{26} - 114 q^{29} - 177 q^{31} - 1191 q^{32} + 24 q^{34} - 82 q^{37} - 1746 q^{38} - 618 q^{41} - 88 q^{43} - 1563 q^{44} - 218 q^{46} - 201 q^{47} - 2955 q^{50} - 36 q^{53} + 538 q^{58} + 747 q^{59} + 1209 q^{61} + 2904 q^{62} - 11168 q^{64} - 2835 q^{65} - 295 q^{67} + 7008 q^{68} + 6 q^{73} - 144 q^{76} + 1019 q^{79} + 4239 q^{80} - 18 q^{82} - 1830 q^{83} + 591 q^{85} - 1342 q^{88} - 4266 q^{89} + 9786 q^{92} + 3 q^{94} - 867 q^{95} - 792 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)