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Properties

Label 2023.4.q
Level $2023$
Weight $4$
Character orbit 2023.q
Rep. character $\chi_{2023}(120,\cdot)$
Character field $\Q(\zeta_{17})$
Dimension $7328$
Sturm bound $816$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.q (of order \(17\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{17})\)
Sturm bound: \(816\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2023, [\chi])\).

Total New Old
Modular forms 9824 7328 2496
Cusp forms 9760 7328 2432
Eisenstein series 64 0 64

Trace form

\( 7328 q - 4 q^{3} - 1800 q^{4} + 120 q^{5} - 64 q^{6} - 3994 q^{9} + O(q^{10}) \) \( 7328 q - 4 q^{3} - 1800 q^{4} + 120 q^{5} - 64 q^{6} - 3994 q^{9} + 908 q^{10} - 52 q^{11} - 48 q^{12} - 152 q^{13} + 80 q^{15} - 8936 q^{16} - 54 q^{17} - 256 q^{18} + 268 q^{19} - 208 q^{20} - 28 q^{21} + 216 q^{22} - 112 q^{23} - 1128 q^{24} - 7198 q^{25} + 72 q^{26} + 518 q^{27} - 584 q^{29} + 192 q^{30} - 56 q^{31} + 620 q^{32} + 200 q^{33} + 54 q^{34} + 280 q^{35} - 14048 q^{36} + 480 q^{37} + 872 q^{38} - 4472 q^{39} + 484 q^{40} - 724 q^{41} + 168 q^{42} - 76 q^{43} - 9720 q^{45} + 2328 q^{46} + 960 q^{47} - 17530 q^{48} - 22442 q^{49} + 2160 q^{50} + 1468 q^{51} + 12900 q^{52} + 3684 q^{53} - 13846 q^{54} + 144 q^{55} - 1400 q^{57} + 3734 q^{58} - 228 q^{59} + 3112 q^{60} - 80 q^{61} - 1216 q^{62} + 112 q^{63} - 29496 q^{64} - 832 q^{65} - 17502 q^{66} + 14246 q^{67} + 378 q^{68} + 344 q^{69} - 728 q^{70} + 536 q^{71} + 21508 q^{72} + 1540 q^{73} - 288 q^{74} - 18612 q^{75} + 22360 q^{76} + 840 q^{77} + 884 q^{78} + 12312 q^{79} - 28236 q^{80} - 46898 q^{81} + 3024 q^{82} - 500 q^{83} + 196 q^{84} - 388 q^{85} + 3772 q^{86} + 576 q^{87} + 19292 q^{88} - 6172 q^{89} - 1068 q^{90} - 336 q^{91} + 12852 q^{92} + 2160 q^{93} - 40436 q^{94} + 584 q^{95} + 29616 q^{96} - 100 q^{97} - 6580 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2023, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2023, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2023, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)