↑

Properties

Label 2023.4.n
Level $2023$
Weight $4$
Character orbit 2023.n
Rep. character $\chi_{2023}(905,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2104$
Sturm bound $816$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.n (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(816\)

Dimensions

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

Total New Old
Modular forms 2520 2216 304
Cusp forms 2376 2104 272
Eisenstein series 144 112 32

Trace form

\( 2104 q + 2 q^{3} + 4100 q^{4} - 6 q^{5} + 40 q^{6} + 8 q^{7} + O(q^{10}) \) \( 2104 q + 2 q^{3} + 4100 q^{4} - 6 q^{5} + 40 q^{6} + 8 q^{7} + 34 q^{10} + 22 q^{11} - 12 q^{12} + 224 q^{13} - 198 q^{14} - 15516 q^{16} - 188 q^{18} - 392 q^{20} - 120 q^{21} + 720 q^{22} - 26 q^{23} - 212 q^{24} + 116 q^{27} + 730 q^{28} - 352 q^{29} - 1860 q^{30} + 90 q^{31} + 1412 q^{33} + 736 q^{35} - 382 q^{37} - 1004 q^{38} - 220 q^{39} - 808 q^{40} - 344 q^{41} + 26 q^{44} + 1264 q^{45} - 508 q^{46} - 1508 q^{47} + 764 q^{48} + 2112 q^{50} - 116 q^{52} + 716 q^{54} + 1648 q^{55} - 7590 q^{56} + 580 q^{57} - 400 q^{58} - 162 q^{61} - 3036 q^{62} + 4468 q^{63} - 116048 q^{64} + 892 q^{65} + 644 q^{67} + 1712 q^{69} + 928 q^{71} + 4236 q^{72} + 1394 q^{73} + 1212 q^{74} + 3852 q^{75} - 764 q^{78} + 166 q^{79} - 958 q^{80} + 67664 q^{81} + 1584 q^{82} - 3276 q^{84} - 4952 q^{86} + 3568 q^{88} - 4908 q^{89} - 7492 q^{90} - 1104 q^{91} - 2400 q^{92} - 1206 q^{95} + 5036 q^{96} + 56 q^{97} + 26920 q^{98} + 3224 q^{99} + O(q^{100}) \)

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

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