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Properties

Label 2023.2.p
Level $2023$
Weight $2$
Character orbit 2023.p
Rep. character $\chi_{2023}(447,\cdot)$
Character field $\Q(\zeta_{16})$
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.p (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{16})\)
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

\( 1328 q + 16 q^{2} + 16 q^{4} + 8 q^{7} + 16 q^{8} + 16 q^{9} + O(q^{10}) \) \( 1328 q + 16 q^{2} + 16 q^{4} + 8 q^{7} + 16 q^{8} + 16 q^{9} - 8 q^{14} + 64 q^{15} - 352 q^{18} - 16 q^{21} + 48 q^{22} + 16 q^{23} + 56 q^{28} + 16 q^{29} - 112 q^{30} - 16 q^{32} - 48 q^{35} + 48 q^{36} - 48 q^{37} + 8 q^{42} + 16 q^{43} + 16 q^{44} - 16 q^{46} - 24 q^{49} - 16 q^{53} - 112 q^{56} + 16 q^{57} + 48 q^{58} - 48 q^{60} - 112 q^{63} - 48 q^{64} + 32 q^{65} - 64 q^{70} - 16 q^{71} + 80 q^{72} + 80 q^{74} - 40 q^{77} - 112 q^{78} + 16 q^{79} + 64 q^{81} - 384 q^{86} + 112 q^{88} + 72 q^{91} - 256 q^{92} - 48 q^{93} + 48 q^{95} + 144 q^{98} - 128 q^{99} + O(q^{100}) \)

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

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