↑

Properties

Label 2394.4.l
Level $2394$
Weight $4$
Character orbit 2394.l
Rep. character $\chi_{2394}(163,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $400$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1920\)

Dimensions

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

Total New Old
Modular forms 2912 400 2512
Cusp forms 2848 400 2448
Eisenstein series 64 0 64

Trace form

\( 400 q - 800 q^{4} - 8 q^{5} - 6 q^{7} + O(q^{10}) \) \( 400 q - 800 q^{4} - 8 q^{5} - 6 q^{7} + 40 q^{10} + 42 q^{11} - 18 q^{13} - 76 q^{14} - 3200 q^{16} + 348 q^{17} + 8 q^{19} + 64 q^{20} + 44 q^{22} + 308 q^{23} - 4916 q^{25} + 152 q^{26} + 24 q^{28} - 86 q^{29} - 88 q^{31} + 152 q^{34} + 700 q^{35} + 326 q^{37} - 72 q^{38} + 160 q^{40} - 582 q^{41} - 136 q^{43} - 336 q^{44} + 236 q^{46} - 620 q^{47} - 786 q^{49} + 416 q^{50} + 144 q^{52} - 94 q^{53} + 202 q^{55} + 128 q^{56} + 168 q^{58} + 4936 q^{59} - 2284 q^{61} + 536 q^{62} + 25600 q^{64} + 160 q^{65} - 534 q^{67} - 696 q^{68} + 824 q^{70} + 1012 q^{71} - 1636 q^{73} + 2032 q^{74} - 376 q^{76} - 1186 q^{77} - 1842 q^{79} - 128 q^{80} - 3648 q^{82} - 3196 q^{83} + 1562 q^{85} + 176 q^{86} + 176 q^{88} + 7192 q^{89} + 4042 q^{91} - 616 q^{92} + 780 q^{94} - 4066 q^{95} + 3724 q^{97} + 3368 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)