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Properties

Label 2023.2.r
Level $2023$
Weight $2$
Character orbit 2023.r
Rep. character $\chi_{2023}(179,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1328$
Sturm bound $408$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2023.r (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(408\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2023, [\chi])\).

Total New Old
Modular forms 1776 1552 224
Cusp forms 1488 1328 160
Eisenstein series 288 224 64

Trace form

\( 1328 q + 4 q^{2} + 4 q^{3} + 16 q^{6} + 8 q^{7} + 32 q^{8} + 4 q^{9} + O(q^{10}) \) \( 1328 q + 4 q^{2} + 4 q^{3} + 16 q^{6} + 8 q^{7} + 32 q^{8} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 28 q^{12} - 32 q^{14} - 24 q^{15} + 504 q^{16} - 24 q^{18} + 4 q^{19} + 48 q^{20} + 48 q^{22} - 8 q^{23} + 28 q^{24} + 8 q^{25} - 36 q^{26} + 64 q^{27} - 32 q^{28} + 16 q^{29} + 4 q^{31} - 48 q^{32} - 56 q^{33} - 144 q^{35} + 32 q^{36} + 36 q^{37} - 16 q^{39} - 28 q^{40} - 40 q^{41} + 28 q^{42} - 16 q^{43} + 20 q^{44} - 8 q^{45} + 4 q^{46} - 56 q^{48} + 68 q^{49} - 64 q^{50} - 40 q^{52} + 20 q^{53} - 24 q^{54} + 28 q^{56} + 16 q^{57} - 28 q^{58} - 4 q^{59} - 76 q^{60} + 24 q^{61} - 88 q^{62} + 20 q^{63} - 8 q^{65} - 12 q^{66} - 8 q^{67} - 544 q^{69} - 76 q^{70} + 32 q^{71} + 24 q^{73} + 28 q^{74} + 108 q^{75} + 8 q^{76} - 160 q^{78} + 4 q^{79} + 44 q^{80} - 24 q^{82} + 88 q^{83} - 344 q^{84} - 168 q^{86} - 68 q^{87} - 104 q^{88} + 48 q^{90} - 64 q^{91} + 80 q^{92} - 8 q^{93} - 44 q^{94} - 48 q^{95} + 12 q^{96} - 80 q^{97} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2023, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2023, [\chi])\) into lower level spaces

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