↑

Properties

Label 2394.4.dk
Level $2394$
Weight $4$
Character orbit 2394.dk
Rep. character $\chi_{2394}(863,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
Sturm bound $1920$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2394.dk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2394, [\chi])\).

Total New Old
Modular forms 2912 320 2592
Cusp forms 2848 320 2528
Eisenstein series 64 0 64

Trace form

\( 320 q - 640 q^{4} + 52 q^{7} + O(q^{10}) \) \( 320 q - 640 q^{4} + 52 q^{7} + 276 q^{13} - 2560 q^{16} - 188 q^{19} + 432 q^{22} + 4072 q^{25} - 176 q^{28} + 708 q^{31} - 720 q^{34} - 3252 q^{37} + 868 q^{43} - 340 q^{49} - 96 q^{55} + 336 q^{58} + 1136 q^{61} + 20480 q^{64} + 2436 q^{67} + 3168 q^{70} - 5192 q^{73} - 752 q^{76} - 5964 q^{79} - 7296 q^{82} + 3096 q^{85} - 1728 q^{88} - 7428 q^{91} + 288 q^{94} + 3816 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2394, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \)