Properties

Label 2023.4.v
Level $2023$
Weight $4$
Character orbit 2023.v
Rep. character $\chi_{2023}(50,\cdot)$
Character field $\Q(\zeta_{34})$
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.v (of order \(34\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{34})\)
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

\( 7328 q - 1848 q^{4} - 136 q^{5} + 4114 q^{9} + O(q^{10}) \) \( 7328 q - 1848 q^{4} - 136 q^{5} + 4114 q^{9} + 1020 q^{10} + 184 q^{13} - 160 q^{15} - 6056 q^{16} + 206 q^{17} + 112 q^{18} - 92 q^{19} + 196 q^{21} + 15358 q^{25} + 72 q^{26} - 918 q^{27} + 288 q^{30} + 620 q^{32} - 1808 q^{33} + 930 q^{34} + 280 q^{35} + 16896 q^{36} - 1200 q^{38} - 5168 q^{39} - 168 q^{42} - 764 q^{43} + 10200 q^{45} + 2448 q^{46} + 560 q^{47} + 20774 q^{48} + 22442 q^{49} - 1704 q^{50} + 2864 q^{51} - 12388 q^{52} + 2412 q^{53} + 4726 q^{54} - 144 q^{55} - 5474 q^{58} + 652 q^{59} - 5888 q^{60} - 5304 q^{62} - 28920 q^{64} - 16654 q^{66} - 8638 q^{67} + 402 q^{68} + 104 q^{69} - 1288 q^{70} - 18348 q^{72} - 23192 q^{76} - 392 q^{77} - 15912 q^{79} + 26860 q^{80} - 31082 q^{81} + 540 q^{83} + 3780 q^{84} + 1908 q^{85} + 1268 q^{86} - 3856 q^{87} - 22032 q^{88} + 3468 q^{89} + 7004 q^{92} + 1888 q^{93} + 31708 q^{94} - 31008 q^{96} + O(q^{100}) \)

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

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