↑

Properties

Label 2394.4.bo
Level $2394$
Weight $4$
Character orbit 2394.bo
Rep. character $\chi_{2394}(125,\cdot)$
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.bo (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

\( 320 q + 640 q^{4} - 56 q^{7} + O(q^{10}) \) \( 320 q + 640 q^{4} - 56 q^{7} - 2560 q^{16} + 144 q^{22} - 4072 q^{25} - 112 q^{28} + 2336 q^{37} - 616 q^{43} - 1728 q^{46} + 1400 q^{49} - 1344 q^{58} - 20480 q^{64} - 1400 q^{67} + 1056 q^{70} - 1064 q^{79} - 4104 q^{85} + 1152 q^{88} + 1500 q^{91} + O(q^{100}) \)

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

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