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Properties

Label 336.6.w
Level $336$
Weight $6$
Character orbit 336.w
Rep. character $\chi_{336}(85,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $240$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 336.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(336, [\chi])\).

Total New Old
Modular forms 648 240 408
Cusp forms 632 240 392
Eisenstein series 16 0 16

Trace form

\( 240 q - 44 q^{4} + O(q^{10}) \) \( 240 q - 44 q^{4} + 200 q^{10} - 1208 q^{11} + 1584 q^{12} + 2156 q^{14} + 3600 q^{15} + 1604 q^{16} + 324 q^{18} - 4720 q^{19} - 1212 q^{22} - 10440 q^{24} + 25960 q^{26} + 8144 q^{29} + 2736 q^{30} - 88320 q^{32} + 14880 q^{34} + 3240 q^{36} - 21296 q^{37} + 74536 q^{38} + 62360 q^{40} - 30760 q^{43} - 74140 q^{44} - 81288 q^{46} - 576240 q^{49} - 57860 q^{50} - 20880 q^{51} + 96688 q^{52} + 49456 q^{53} + 29160 q^{54} + 75460 q^{56} + 10076 q^{58} - 49464 q^{60} - 96160 q^{61} - 175632 q^{62} - 31752 q^{63} - 137060 q^{64} + 110752 q^{65} - 12232 q^{67} + 296312 q^{68} + 44640 q^{69} + 71736 q^{70} + 28836 q^{72} + 49620 q^{74} + 193248 q^{75} - 439432 q^{76} + 14896 q^{77} - 151416 q^{78} + 143920 q^{79} - 492880 q^{80} - 1574640 q^{81} - 319320 q^{82} + 252880 q^{83} - 264800 q^{85} + 210636 q^{86} + 249972 q^{88} + 92016 q^{90} - 641808 q^{92} - 663736 q^{94} - 302040 q^{96} - 97848 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)