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Properties

Label 252.9.bl
Level $252$
Weight $9$
Character orbit 252.bl
Rep. character $\chi_{252}(67,\cdot)$
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.bl (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

\( 760 q + q^{2} + q^{4} - 4 q^{5} + 252 q^{6} - 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 760 q + q^{2} + q^{4} - 4 q^{5} + 252 q^{6} - 8 q^{8} - 2 q^{9} - 514 q^{10} - 68553 q^{12} - 4 q^{13} + 17157 q^{14} + q^{16} - 4 q^{17} - 289339 q^{18} - 131074 q^{20} - 315456 q^{21} + 510 q^{22} + 87130 q^{24} + 56874996 q^{25} + 254 q^{26} + 65532 q^{28} + 632540 q^{29} - 2387840 q^{30} + 1079221 q^{32} + 52486 q^{33} + 254 q^{34} - 2643070 q^{36} - 4 q^{37} + 6434994 q^{38} - 781252 q^{40} - 4 q^{41} - 3149545 q^{42} + 6307053 q^{44} - 4705002 q^{45} + 510 q^{46} - 19160593 q^{48} - 2 q^{49} - 15475269 q^{50} + 262142 q^{52} - 4 q^{53} - 59507266 q^{54} - 72267822 q^{56} - 9885772 q^{57} + 1022 q^{58} + 11241128 q^{60} + 2 q^{61} - 99425988 q^{62} - 8 q^{64} - 3304130 q^{65} - 36855903 q^{66} - 17453308 q^{68} - 3824262 q^{69} + 4201788 q^{70} - 123388003 q^{72} - 4 q^{73} - 315958006 q^{74} - 65538 q^{76} + 57820230 q^{77} - 6065003 q^{78} + 85297355 q^{80} + 120860318 q^{81} + 254 q^{82} - 226207333 q^{84} + 781246 q^{85} + 16791582 q^{86} + 33554430 q^{88} + 73646876 q^{89} - 56943199 q^{90} + 257916084 q^{92} - 136277766 q^{93} - 1023 q^{94} + 281160508 q^{96} - 4 q^{97} - 260771183 q^{98} + O(q^{100}) \)

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.