↑

Properties

Label 392.4.x
Level $392$
Weight $4$
Character orbit 392.x
Rep. character $\chi_{392}(29,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $996$
Sturm bound $224$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 392.x (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(392, [\chi])\).

Total New Old
Modular forms 1020 1020 0
Cusp forms 996 996 0
Eisenstein series 24 24 0

Trace form

\( 996 q - 5 q^{2} - 5 q^{4} - 21 q^{6} - 12 q^{7} - 47 q^{8} + 1448 q^{9} + O(q^{10}) \) \( 996 q - 5 q^{2} - 5 q^{4} - 21 q^{6} - 12 q^{7} - 47 q^{8} + 1448 q^{9} - 27 q^{10} - 334 q^{12} - 233 q^{14} - 118 q^{15} + 51 q^{16} - 10 q^{17} + 20 q^{18} - 267 q^{20} - 273 q^{22} - 10 q^{23} - 259 q^{24} + 3940 q^{25} + 45 q^{26} + 128 q^{28} + 36 q^{30} + 2208 q^{31} + 555 q^{32} - 118 q^{33} + 1131 q^{34} + 769 q^{36} + 227 q^{38} - 118 q^{39} - 1395 q^{40} - 10 q^{41} + 287 q^{42} - 2443 q^{44} + 781 q^{46} - 1358 q^{47} + 988 q^{48} + 348 q^{49} - 4824 q^{50} - 19 q^{52} - 2198 q^{54} + 370 q^{55} - 1388 q^{56} - 76 q^{57} + 301 q^{58} + 1849 q^{60} + 657 q^{62} + 600 q^{63} - 1811 q^{64} - 510 q^{65} - 5783 q^{66} + 1296 q^{68} + 3367 q^{70} + 550 q^{71} - 4838 q^{72} + 422 q^{73} - 1295 q^{74} + 4718 q^{76} + 2913 q^{78} - 24 q^{79} - 6508 q^{80} - 15348 q^{81} + 2170 q^{82} - 7490 q^{84} + 5005 q^{86} + 1970 q^{87} + 1421 q^{88} - 858 q^{89} - 3336 q^{90} + 9328 q^{92} + 578 q^{94} + 5104 q^{95} + 12782 q^{96} - 3096 q^{97} - 16329 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(392, [\chi])\) into newform subspaces

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