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Properties

Label 336.6.u
Level $336$
Weight $6$
Character orbit 336.u
Rep. character $\chi_{336}(139,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $320$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 648 320 328
Cusp forms 632 320 312
Eisenstein series 16 0 16

Trace form

\( 320 q + 44 q^{4} + 984 q^{8} + O(q^{10}) \) \( 320 q + 44 q^{4} + 984 q^{8} - 1208 q^{11} - 2480 q^{14} + 836 q^{16} + 324 q^{18} - 16852 q^{22} - 3344 q^{23} - 6112 q^{28} + 8144 q^{29} - 4776 q^{35} - 21296 q^{37} + 14220 q^{42} - 32072 q^{43} - 52116 q^{44} + 100040 q^{46} - 119564 q^{50} - 49456 q^{53} - 83132 q^{56} - 17732 q^{58} + 49464 q^{60} + 226124 q^{64} - 166280 q^{67} + 123656 q^{70} + 575360 q^{71} + 28836 q^{72} - 237348 q^{74} - 248832 q^{78} - 2099520 q^{81} - 116856 q^{84} + 951700 q^{86} + 682828 q^{88} - 429496 q^{91} - 404632 q^{92} - 333248 q^{98} + 97848 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(336, [\chi]) \cong \)