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Properties

Label 336.9.bt
Level $336$
Weight $9$
Character orbit 336.bt
Rep. character $\chi_{336}(53,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2032$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 336.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(336, [\chi])\).

Total New Old
Modular forms 2064 2064 0
Cusp forms 2032 2032 0
Eisenstein series 32 32 0

Trace form

\( 2032 q - 2 q^{3} - 4 q^{4} - 8 q^{6} + O(q^{10}) \) \( 2032 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 16 q^{15} + 222700 q^{16} - 288828 q^{18} - 4 q^{19} - 13126 q^{21} - 909208 q^{22} - 161142 q^{24} - 8 q^{27} - 1391172 q^{28} - 1983070 q^{30} - 8 q^{31} - 4 q^{33} - 3187504 q^{34} + 3338048 q^{36} - 4 q^{37} - 10742840 q^{40} + 15228290 q^{42} - 16 q^{43} + 1562498 q^{45} + 2044 q^{46} + 63141672 q^{48} - 16 q^{49} - 15120966 q^{51} + 11487032 q^{52} + 25893838 q^{54} - 37304420 q^{58} + 22557646 q^{60} - 4 q^{61} - 23059212 q^{63} + 48383936 q^{64} - 20791246 q^{66} + 74704380 q^{67} + 26236 q^{69} + 103989012 q^{70} + 6809890 q^{72} + 755004 q^{75} + 279013904 q^{76} - 139674444 q^{78} - 8 q^{79} - 4 q^{81} - 17450928 q^{82} - 19732636 q^{84} - 3125016 q^{85} + 83571180 q^{88} + 264448108 q^{90} + 221318784 q^{91} + 26242 q^{93} + 76915536 q^{94} + 262579428 q^{96} - 32 q^{97} + 172186876 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

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