↑

Properties

Label 2023.4.r
Level $2023$
Weight $4$
Character orbit 2023.r
Rep. character $\chi_{2023}(179,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $4208$
Sturm bound $816$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.r (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(816\)

Dimensions

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

Total New Old
Modular forms 5040 4432 608
Cusp forms 4752 4208 544
Eisenstein series 288 224 64

Trace form

\( 4208 q + 4 q^{2} + 4 q^{3} + 20 q^{5} + 16 q^{6} + 8 q^{7} + 80 q^{8} + 4 q^{9} + O(q^{10}) \) \( 4208 q + 4 q^{2} + 4 q^{3} + 20 q^{5} + 16 q^{6} + 8 q^{7} + 80 q^{8} + 4 q^{9} + 4 q^{10} + 60 q^{11} + 220 q^{12} + 504 q^{14} + 192 q^{15} + 30984 q^{16} - 504 q^{18} + 4 q^{19} + 528 q^{20} - 1216 q^{22} + 172 q^{23} + 748 q^{24} + 228 q^{25} - 764 q^{26} - 1088 q^{27} + 80 q^{28} + 16 q^{29} + 4 q^{31} - 176 q^{32} + 72 q^{33} + 880 q^{35} + 464 q^{36} + 100 q^{37} - 760 q^{39} - 60 q^{40} - 1200 q^{41} + 1932 q^{42} + 1264 q^{43} + 2004 q^{44} - 908 q^{45} + 1348 q^{46} + 3832 q^{48} - 1248 q^{49} - 4032 q^{50} - 3064 q^{52} - 476 q^{53} + 1848 q^{54} + 444 q^{56} + 16 q^{57} - 764 q^{58} - 492 q^{59} + 1220 q^{60} - 1252 q^{61} - 1848 q^{62} + 5804 q^{63} - 2800 q^{65} - 60 q^{66} - 216 q^{67} + 21088 q^{69} - 5404 q^{70} - 2320 q^{71} + 964 q^{73} - 4468 q^{74} - 1980 q^{75} + 312 q^{76} - 7016 q^{77} + 11040 q^{78} - 1356 q^{79} - 7180 q^{80} + 6752 q^{82} - 2032 q^{83} - 8216 q^{84} - 17672 q^{86} - 3692 q^{87} + 3512 q^{88} + 7200 q^{90} - 4336 q^{91} + 1536 q^{92} - 2588 q^{93} + 4580 q^{94} + 1436 q^{95} + 4260 q^{96} + 4624 q^{97} - 29528 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2023, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)