↑

Properties

Label 3192.2.fr
Level $3192$
Weight $2$
Character orbit 3192.fr
Rep. character $\chi_{3192}(2501,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1264$
Sturm bound $1280$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3192.fr (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3192 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3192, [\chi])\).

Total New Old
Modular forms 1296 1296 0
Cusp forms 1264 1264 0
Eisenstein series 32 32 0

Trace form

\( 1264 q - 4 q^{4} + 2 q^{6} - 16 q^{7} + 2 q^{9} + O(q^{10}) \) \( 1264 q - 4 q^{4} + 2 q^{6} - 16 q^{7} + 2 q^{9} + 18 q^{12} - 12 q^{15} - 4 q^{16} - 12 q^{18} - 2 q^{24} + 1192 q^{25} - 10 q^{28} - q^{30} - 12 q^{34} + 2 q^{39} - 14 q^{42} - 24 q^{46} + 27 q^{48} - 8 q^{49} - 6 q^{52} - 42 q^{54} + 12 q^{55} - 14 q^{57} - 32 q^{58} - 42 q^{60} + 26 q^{63} + 32 q^{64} + 2 q^{66} + 36 q^{70} + 15 q^{72} + 12 q^{73} - 72 q^{76} + 27 q^{78} + 2 q^{81} - 54 q^{82} + 21 q^{84} - 10 q^{87} + 36 q^{88} + 39 q^{90} + 12 q^{94} + 2 q^{96} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3192, [\chi])\) into newform subspaces

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