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Properties

Label 2394.4.r
Level $2394$
Weight $4$
Character orbit 2394.r
Rep. character $\chi_{2394}(919,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $400$
Sturm bound $1920$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2394.r (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

\( 400 q + 1600 q^{4} + 16 q^{5} - 6 q^{7} + O(q^{10}) \) \( 400 q + 1600 q^{4} + 16 q^{5} - 6 q^{7} - 80 q^{10} + 42 q^{11} - 18 q^{13} + 32 q^{14} + 6400 q^{16} - 174 q^{17} - 94 q^{19} + 64 q^{20} + 44 q^{22} - 154 q^{23} + 9832 q^{25} + 152 q^{26} - 24 q^{28} - 86 q^{29} - 88 q^{31} + 152 q^{34} - 374 q^{35} + 326 q^{37} + 36 q^{38} - 320 q^{40} - 582 q^{41} - 136 q^{43} + 168 q^{44} + 236 q^{46} + 310 q^{47} - 786 q^{49} + 416 q^{50} - 72 q^{52} + 188 q^{53} + 202 q^{55} + 128 q^{56} + 168 q^{58} - 2468 q^{59} + 1142 q^{61} + 536 q^{62} + 25600 q^{64} + 160 q^{65} + 1068 q^{67} - 696 q^{68} - 1648 q^{70} + 1012 q^{71} + 818 q^{73} - 1016 q^{74} - 376 q^{76} - 1186 q^{77} + 3684 q^{79} + 256 q^{80} + 1824 q^{82} - 3196 q^{83} + 1562 q^{85} - 88 q^{86} + 176 q^{88} - 3596 q^{89} - 1838 q^{91} - 616 q^{92} + 780 q^{94} + 7814 q^{95} + 3724 q^{97} + 416 q^{98} + O(q^{100}) \)

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

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