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Properties

Label 1323.4.h
Level $1323$
Weight $4$
Character orbit 1323.h
Rep. character $\chi_{1323}(226,\cdot)$
Character field $\Q(\zeta_{3})$
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.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 232 q - 2 q^{2} + 898 q^{4} - 19 q^{5} + O(q^{10}) \) \( 232 q - 2 q^{2} + 898 q^{4} - 19 q^{5} + 18 q^{10} + 9 q^{11} + 14 q^{13} + 3346 q^{16} - 162 q^{17} - 58 q^{19} - 362 q^{20} + 12 q^{22} - 145 q^{23} - 2501 q^{25} - 266 q^{26} + 462 q^{29} + 122 q^{31} + 58 q^{32} - 6 q^{34} + 86 q^{37} - 761 q^{38} + 18 q^{40} - 692 q^{41} + 80 q^{43} + 5 q^{44} + 222 q^{46} + 2010 q^{47} + 489 q^{50} + 335 q^{52} + 434 q^{53} + 870 q^{55} - 237 q^{58} + 3330 q^{59} + 878 q^{61} + 1812 q^{62} + 11392 q^{64} + 1170 q^{65} + 590 q^{67} - 1374 q^{68} + 1668 q^{71} + 338 q^{73} + 2077 q^{74} - 1006 q^{76} + 1202 q^{79} - 4817 q^{80} - 6 q^{82} - 1356 q^{83} - 849 q^{85} - 4333 q^{86} - 417 q^{88} - 2200 q^{89} - 1322 q^{92} - 2382 q^{94} - 12706 q^{95} + 266 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1323, [\chi]) \cong \)