Properties

Label 2023.4.w
Level $2023$
Weight $4$
Character orbit 2023.w
Rep. character $\chi_{2023}(40,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $8416$
Sturm bound $816$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.w (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(816\)

Dimensions

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

Total New Old
Modular forms 10080 8864 1216
Cusp forms 9504 8416 1088
Eisenstein series 576 448 128

Trace form

\( 8416 q + 8 q^{2} + 24 q^{3} + 8 q^{4} + 24 q^{5} + 16 q^{7} + 32 q^{8} + 8 q^{9} + O(q^{10}) \) \( 8416 q + 8 q^{2} + 24 q^{3} + 8 q^{4} + 24 q^{5} + 16 q^{7} + 32 q^{8} + 8 q^{9} + 24 q^{10} - 104 q^{11} + 24 q^{12} - 144 q^{14} + 704 q^{15} + 784 q^{18} + 24 q^{19} + 112 q^{21} - 416 q^{22} + 8 q^{23} + 24 q^{24} - 440 q^{25} + 24 q^{26} + 160 q^{28} + 32 q^{29} + 1352 q^{30} + 24 q^{31} + 136 q^{32} + 1760 q^{35} - 96 q^{36} + 680 q^{37} + 24 q^{38} + 1320 q^{39} + 24 q^{40} - 3968 q^{42} + 32 q^{43} - 1944 q^{44} + 24 q^{45} - 952 q^{46} + 24 q^{47} + 3088 q^{49} - 336 q^{52} - 1400 q^{53} - 13776 q^{54} + 5816 q^{56} + 32 q^{57} - 184 q^{58} + 24 q^{59} + 2568 q^{60} + 3624 q^{61} - 9584 q^{63} + 1056 q^{64} - 2552 q^{65} + 24 q^{66} - 5416 q^{70} + 3168 q^{71} - 1016 q^{72} - 5736 q^{73} - 1656 q^{74} + 3192 q^{75} + 1120 q^{77} - 5344 q^{78} + 8 q^{79} + 15384 q^{80} + 3464 q^{81} - 17136 q^{82} + 22128 q^{86} + 11256 q^{87} + 6920 q^{88} + 24 q^{89} - 560 q^{91} - 1984 q^{92} - 1848 q^{93} - 1128 q^{94} - 824 q^{95} + 5208 q^{96} + 12120 q^{98} + 42384 q^{99} + O(q^{100}) \)

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

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