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Properties

Label 2023.4.bi
Level $2023$
Weight $4$
Character orbit 2023.bi
Rep. character $\chi_{2023}(6,\cdot)$
Character field $\Q(\zeta_{272})$
Dimension $78080$
Sturm bound $816$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.bi (of order \(272\) and degree \(128\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2023 \)
Character field: \(\Q(\zeta_{272})\)
Sturm bound: \(816\)

Dimensions

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

Total New Old
Modular forms 78592 78592 0
Cusp forms 78080 78080 0
Eisenstein series 512 512 0

Trace form

\( 78080 q - 256 q^{2} - 256 q^{4} - 128 q^{7} - 256 q^{8} - 256 q^{9} + O(q^{10}) \) \( 78080 q - 256 q^{2} - 256 q^{4} - 128 q^{7} - 256 q^{8} - 256 q^{9} - 480 q^{11} + 32 q^{14} - 928 q^{15} - 272 q^{16} - 240 q^{18} - 224 q^{21} + 192 q^{22} - 256 q^{23} - 1152 q^{25} - 272 q^{28} - 256 q^{29} + 2432 q^{30} - 384 q^{32} - 120 q^{35} - 128 q^{36} + 1088 q^{37} - 1568 q^{39} + 688 q^{42} - 256 q^{43} - 5696 q^{44} + 704 q^{46} + 1408 q^{49} - 272 q^{50} - 1856 q^{51} + 1152 q^{53} - 1128 q^{56} - 256 q^{57} - 64 q^{58} - 2816 q^{60} + 1840 q^{63} - 1280 q^{64} + 2304 q^{65} - 272 q^{67} + 5304 q^{70} - 3392 q^{71} + 768 q^{72} + 1408 q^{74} - 1232 q^{77} + 5120 q^{78} - 256 q^{79} - 3712 q^{81} - 136 q^{84} + 2336 q^{85} - 240 q^{86} - 7168 q^{88} + 448 q^{91} + 5456 q^{92} + 1600 q^{93} + 576 q^{95} - 12232 q^{98} + 6448 q^{99} + O(q^{100}) \)

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.