↑

Properties

Label 3332.2.cj
Level $3332$
Weight $2$
Character orbit 3332.cj
Rep. character $\chi_{3332}(83,\cdot)$
Character field $\Q(\zeta_{56})$
Dimension $12000$
Sturm bound $1008$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.cj (of order \(56\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3332 \)
Character field: \(\Q(\zeta_{56})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3332, [\chi])\).

Total New Old
Modular forms 12192 12192 0
Cusp forms 12000 12000 0
Eisenstein series 192 192 0

Trace form

\( 12000 q - 20 q^{2} - 56 q^{5} - 28 q^{6} - 20 q^{8} - 40 q^{9} + O(q^{10}) \) \( 12000 q - 20 q^{2} - 56 q^{5} - 28 q^{6} - 20 q^{8} - 40 q^{9} - 28 q^{10} - 28 q^{12} - 8 q^{14} - 40 q^{16} - 56 q^{17} - 96 q^{18} - 28 q^{20} - 68 q^{22} - 28 q^{24} - 40 q^{25} - 28 q^{26} + 136 q^{28} - 40 q^{29} - 60 q^{32} - 112 q^{33} - 28 q^{34} - 52 q^{36} - 40 q^{37} - 252 q^{40} - 56 q^{41} - 76 q^{42} - 68 q^{44} - 56 q^{45} - 20 q^{46} - 48 q^{49} - 96 q^{50} - 56 q^{52} - 40 q^{53} + 56 q^{54} - 72 q^{56} - 40 q^{57} - 20 q^{58} + 12 q^{60} - 56 q^{61} - 28 q^{62} + 40 q^{65} - 28 q^{66} - 336 q^{69} - 108 q^{70} - 56 q^{73} - 20 q^{74} + 84 q^{76} + 16 q^{77} + 76 q^{78} + 112 q^{82} - 168 q^{84} - 40 q^{85} + 24 q^{86} - 240 q^{88} - 252 q^{90} + 12 q^{92} - 40 q^{93} - 364 q^{94} - 28 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

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