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Properties

Label 2023.4.z
Level $2023$
Weight $4$
Character orbit 2023.z
Rep. character $\chi_{2023}(64,\cdot)$
Character field $\Q(\zeta_{68})$
Dimension $14656$
Sturm bound $816$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.z (of order \(68\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{68})\)
Sturm bound: \(816\)

Dimensions

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

Total New Old
Modular forms 19648 14656 4992
Cusp forms 19520 14656 4864
Eisenstein series 128 0 128

Trace form

\( 14656 q + 4 q^{3} + 3648 q^{4} + 16 q^{5} + 16 q^{6} + O(q^{10}) \) \( 14656 q + 4 q^{3} + 3648 q^{4} + 16 q^{5} + 16 q^{6} - 1912 q^{10} - 148 q^{11} - 48 q^{12} + 32 q^{13} - 13936 q^{16} - 24 q^{17} + 576 q^{18} - 208 q^{20} - 168 q^{21} - 216 q^{22} - 96 q^{23} - 744 q^{24} - 9248 q^{25} + 184 q^{27} - 168 q^{29} - 480 q^{30} + 1400 q^{31} + 1608 q^{33} + 1704 q^{34} + 560 q^{35} - 1264 q^{37} - 328 q^{38} - 10376 q^{39} - 668 q^{40} - 1388 q^{41} + 1536 q^{44} - 1280 q^{45} - 7320 q^{46} + 1520 q^{47} + 1644 q^{48} + 2344 q^{50} - 4476 q^{51} - 512 q^{52} - 7888 q^{53} + 38896 q^{54} - 2488 q^{57} + 932 q^{58} + 2768 q^{61} - 15808 q^{62} + 112 q^{63} + 55248 q^{64} + 3472 q^{65} + 41820 q^{66} - 3464 q^{67} + 84 q^{68} - 448 q^{69} + 1064 q^{71} - 2024 q^{72} - 676 q^{73} + 2584 q^{74} + 17020 q^{75} - 2988 q^{78} + 3936 q^{79} - 3608 q^{80} + 68556 q^{81} - 2864 q^{82} + 56 q^{84} - 2432 q^{85} + 1840 q^{86} + 2740 q^{88} + 496 q^{89} + 9868 q^{90} - 336 q^{91} - 11704 q^{92} - 440 q^{95} + 6512 q^{96} + 172 q^{97} - 784 q^{98} - 5180 q^{99} + O(q^{100}) \)

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

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