↑

Properties

Label 2394.4.by
Level $2394$
Weight $4$
Character orbit 2394.by
Rep. character $\chi_{2394}(647,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.by (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 288 2624
Cusp forms 2848 288 2560
Eisenstein series 64 0 64

Trace form

\( 288 q + 576 q^{4} + 24 q^{7} + O(q^{10}) \) \( 288 q + 576 q^{4} + 24 q^{7} - 144 q^{10} - 2304 q^{16} + 672 q^{22} - 3432 q^{25} - 96 q^{28} + 1656 q^{31} - 576 q^{40} - 576 q^{43} - 480 q^{46} + 2472 q^{49} - 432 q^{58} - 18432 q^{64} + 1488 q^{67} - 336 q^{70} + 1152 q^{73} - 1512 q^{79} + 1728 q^{82} + 9408 q^{85} + 1344 q^{88} + 1536 q^{91} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)