Properties

Label 289.10.b
Level $289$
Weight $10$
Character orbit 289.b
Rep. character $\chi_{289}(288,\cdot)$
Character field $\Q$
Dimension $196$
Sturm bound $255$

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Defining parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Sturm bound: \(255\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(289, [\chi])\).

Total New Old
Modular forms 238 210 28
Cusp forms 220 196 24
Eisenstein series 18 14 4

Trace form

\( 196 q - 30 q^{2} + 49326 q^{4} - 23550 q^{8} - 1250528 q^{9} + O(q^{10}) \) \( 196 q - 30 q^{2} + 49326 q^{4} - 23550 q^{8} - 1250528 q^{9} + 81276 q^{13} + 342948 q^{15} + 12019646 q^{16} - 781130 q^{18} - 1335564 q^{19} - 349080 q^{21} - 65148156 q^{25} - 3173452 q^{26} + 6033406 q^{30} + 10066040 q^{32} + 10892288 q^{33} - 3263076 q^{35} - 298607000 q^{36} - 37450024 q^{38} - 1743798 q^{42} + 7682408 q^{43} + 120300956 q^{47} - 1039423120 q^{49} + 265194992 q^{50} + 77598892 q^{52} - 17605356 q^{53} - 396967948 q^{55} - 63223608 q^{59} - 124611682 q^{60} + 2980801034 q^{64} + 153911820 q^{66} + 306835716 q^{67} + 259223152 q^{69} - 267636100 q^{70} - 672413680 q^{72} - 279858964 q^{76} + 221860840 q^{77} + 6371660356 q^{81} + 838832380 q^{83} - 1426796580 q^{84} - 547504634 q^{86} - 1027451320 q^{87} + 996631200 q^{89} - 1522715168 q^{93} - 195733572 q^{94} + 365165008 q^{98} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(289, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(289, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(289, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)