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Properties

Label 252.9.s
Level $252$
Weight $9$
Character orbit 252.s
Rep. character $\chi_{252}(83,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $760$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(252, [\chi])\).

Total New Old
Modular forms 776 776 0
Cusp forms 760 760 0
Eisenstein series 16 16 0

Trace form

\( 760 q - 6 q^{2} - 2 q^{4} - 8 q^{9} + O(q^{10}) \) \( 760 q - 6 q^{2} - 2 q^{4} - 8 q^{9} - 26508 q^{14} - 2 q^{16} + 289334 q^{18} - 157730 q^{21} + 1022 q^{22} - 28437504 q^{25} - 131076 q^{28} + 3795252 q^{29} + 1747304 q^{30} - 4836156 q^{32} - 5924042 q^{36} - 16 q^{37} - 4184390 q^{42} + 1016 q^{46} - 2 q^{49} + 2343744 q^{50} + 38991180 q^{56} + 9807024 q^{57} - 1026 q^{58} + 26493332 q^{60} - 8 q^{64} - 5224908 q^{65} - 4983808 q^{70} + 84374060 q^{72} - 146576208 q^{74} - 35105478 q^{77} + 13172220 q^{78} - 57645128 q^{81} + 224138774 q^{84} - 1562504 q^{85} - 336172380 q^{86} - 33554434 q^{88} - 562614306 q^{92} - 136225284 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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