↑

Properties

Label 392.6.b
Level $392$
Weight $6$
Character orbit 392.b
Rep. character $\chi_{392}(197,\cdot)$
Character field $\Q$
Dimension $200$
Sturm bound $336$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 392.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(392, [\chi])\).

Total New Old
Modular forms 288 210 78
Cusp forms 272 200 72
Eisenstein series 16 10 6

Trace form

\( 200 q + 2 q^{2} - 178 q^{6} - 184 q^{8} - 15388 q^{9} + O(q^{10}) \) \( 200 q + 2 q^{2} - 178 q^{6} - 184 q^{8} - 15388 q^{9} + 36 q^{10} + 2 q^{12} - 1396 q^{15} - 460 q^{16} + 204 q^{17} - 678 q^{18} - 388 q^{20} + 8132 q^{22} + 4012 q^{23} - 13894 q^{24} - 110940 q^{25} + 5516 q^{26} + 6144 q^{30} - 1392 q^{31} - 1908 q^{32} - 3320 q^{33} + 4642 q^{34} - 39056 q^{36} - 25218 q^{38} + 34136 q^{39} + 9340 q^{40} - 4564 q^{41} - 10828 q^{44} + 4284 q^{46} + 54720 q^{47} - 41910 q^{48} - 8710 q^{50} + 18660 q^{52} + 16780 q^{54} + 24576 q^{55} - 28788 q^{57} - 99828 q^{58} + 76020 q^{60} - 117088 q^{62} + 51780 q^{64} - 32016 q^{65} + 74212 q^{66} - 149674 q^{68} - 65552 q^{71} + 288852 q^{72} - 65156 q^{73} + 151720 q^{74} + 276642 q^{76} + 50212 q^{78} - 54628 q^{79} - 3716 q^{80} + 1015040 q^{81} - 52198 q^{82} - 23932 q^{86} + 125248 q^{87} + 89836 q^{88} - 90948 q^{89} + 660204 q^{90} - 80684 q^{92} + 110304 q^{94} - 196316 q^{95} + 303514 q^{96} + 179980 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(392, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(392, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(392, [\chi]) \cong \)