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Properties

Label 196.6.j
Level $196$
Weight $6$
Character orbit 196.j
Rep. character $\chi_{196}(27,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $828$
Sturm bound $168$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 196.j (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(196, [\chi])\).

Total New Old
Modular forms 852 852 0
Cusp forms 828 828 0
Eisenstein series 24 24 0

Trace form

\( 828 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 251 q^{8} - 10864 q^{9} + O(q^{10}) \) \( 828 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 251 q^{8} - 10864 q^{9} - 7 q^{10} - 3822 q^{12} - 14 q^{13} - 4375 q^{14} + 755 q^{16} - 14 q^{17} + 4548 q^{18} - 7 q^{20} + 1778 q^{21} + 4959 q^{22} + 371 q^{24} + 78512 q^{25} - 7 q^{26} - 18130 q^{28} + 19890 q^{29} - 3104 q^{30} - 5605 q^{32} - 14 q^{33} - 58331 q^{34} - 21251 q^{36} + 5370 q^{37} - 231 q^{38} + 105217 q^{40} - 14 q^{41} - 7623 q^{42} - 32391 q^{44} - 14 q^{45} - 10899 q^{46} + 24752 q^{49} - 294372 q^{50} - 7 q^{52} + 17502 q^{53} + 1694 q^{54} + 265986 q^{56} + 36224 q^{57} + 75149 q^{58} + 99813 q^{60} + 175518 q^{61} - 231 q^{62} - 22091 q^{64} - 54710 q^{65} - 635887 q^{66} - 221158 q^{69} + 331527 q^{70} + 176250 q^{72} - 14 q^{73} - 178523 q^{74} + 66430 q^{76} - 113834 q^{77} - 86555 q^{78} - 238980 q^{81} + 510188 q^{82} - 342342 q^{84} - 28326 q^{85} - 316637 q^{86} - 374287 q^{88} - 14 q^{89} - 383138 q^{90} - 187370 q^{92} + 331408 q^{93} + 618674 q^{94} + 748174 q^{96} + 1212365 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

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