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Properties

Label 2023.4.p
Level $2023$
Weight $4$
Character orbit 2023.p
Rep. character $\chi_{2023}(447,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $4208$
Sturm bound $816$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.p (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{16})\)
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

\( 4208 q + 16 q^{2} + 16 q^{4} + 8 q^{7} + 16 q^{8} + 16 q^{9} + O(q^{10}) \) \( 4208 q + 16 q^{2} + 16 q^{4} + 8 q^{7} + 16 q^{8} + 16 q^{9} - 208 q^{11} + 168 q^{14} - 656 q^{15} + 1568 q^{18} - 88 q^{21} + 464 q^{22} + 16 q^{23} - 880 q^{25} - 136 q^{28} + 16 q^{29} + 2704 q^{30} - 112 q^{32} - 2096 q^{35} + 144 q^{36} + 1360 q^{37} - 1296 q^{39} + 824 q^{42} + 16 q^{43} - 5424 q^{44} + 976 q^{46} + 1544 q^{49} + 1424 q^{53} - 992 q^{56} + 16 q^{57} + 208 q^{58} - 2544 q^{60} + 1976 q^{63} - 1008 q^{64} + 2576 q^{65} + 5440 q^{70} - 3120 q^{71} + 1040 q^{72} + 1680 q^{74} - 1096 q^{77} + 5392 q^{78} + 16 q^{79} - 3440 q^{81} - 22464 q^{86} - 6896 q^{88} + 584 q^{91} + 5728 q^{92} + 1872 q^{93} + 848 q^{95} - 12096 q^{98} + 6720 q^{99} + O(q^{100}) \)

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

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