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Properties

Label 252.9.bn
Level $252$
Weight $9$
Character orbit 252.bn
Rep. character $\chi_{252}(47,\cdot)$
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.bn (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

\( 760 q - 3 q^{2} + q^{4} - 12 q^{5} + 768 q^{6} - 2 q^{9} + O(q^{10}) \) \( 760 q - 3 q^{2} + q^{4} - 12 q^{5} + 768 q^{6} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} + q^{16} + 289337 q^{18} + 315448 q^{21} - 514 q^{22} - 19686 q^{24} + 56874996 q^{25} - 768 q^{26} + 65532 q^{28} - 1897644 q^{29} - 2360572 q^{30} + 4836147 q^{32} - 6 q^{33} - 768 q^{34} + 4312090 q^{36} - 4 q^{37} - 19308066 q^{38} + 8996305 q^{42} + 18134733 q^{44} + 4739994 q^{45} - 514 q^{46} - 19683 q^{48} - 2 q^{49} - 1171881 q^{50} + 50353140 q^{54} - 73579992 q^{56} + 9885756 q^{57} - 1026 q^{58} - 14615152 q^{60} - 6 q^{61} + 1536 q^{62} - 8 q^{64} + 5224890 q^{65} - 5038851 q^{66} + 53146344 q^{68} - 39366 q^{69} - 7326790 q^{70} - 26504071 q^{72} - 12 q^{73} - 196608 q^{76} - 35105478 q^{77} + 57053751 q^{78} - 258235821 q^{80} + 28822558 q^{81} + 762 q^{82} - 50428273 q^{84} + 781246 q^{85} - 33554434 q^{88} + 220940640 q^{89} + 326303607 q^{90} + 281307144 q^{92} - 136225278 q^{93} - 3 q^{94} + 175815306 q^{96} - 450938739 q^{98} + O(q^{100}) \)

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.