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Properties

Label 2023.2.b
Level $2023$
Weight $2$
Character orbit 2023.b
Rep. character $\chi_{2023}(288,\cdot)$
Character field $\Q$
Dimension $134$
Sturm bound $408$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2023.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Sturm bound: \(408\)

Dimensions

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

Total New Old
Modular forms 222 134 88
Cusp forms 186 134 52
Eisenstein series 36 0 36

Trace form

\( 134 q + 4 q^{2} + 140 q^{4} + 12 q^{8} - 138 q^{9} + O(q^{10}) \) \( 134 q + 4 q^{2} + 140 q^{4} + 12 q^{8} - 138 q^{9} + 4 q^{13} + 12 q^{15} + 136 q^{16} - 12 q^{18} - 138 q^{25} - 12 q^{26} - 20 q^{30} + 28 q^{32} + 16 q^{33} - 8 q^{35} - 144 q^{36} + 4 q^{38} + 24 q^{42} - 12 q^{43} - 134 q^{49} - 16 q^{50} + 48 q^{52} - 8 q^{53} - 8 q^{55} - 56 q^{59} + 52 q^{60} + 144 q^{64} - 72 q^{66} - 40 q^{67} - 32 q^{69} - 4 q^{70} - 20 q^{72} + 28 q^{76} + 134 q^{81} + 20 q^{83} - 24 q^{84} + 56 q^{86} + 76 q^{87} - 4 q^{89} - 24 q^{93} + 28 q^{94} - 4 q^{98} + O(q^{100}) \)

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

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