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Properties

Label 2394.4.z
Level $2394$
Weight $4$
Character orbit 2394.z
Rep. character $\chi_{2394}(145,\cdot)$
Character field $\Q(\zeta_{6})$
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.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
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 400 2512
Cusp forms 2848 400 2448
Eisenstein series 64 0 64

Trace form

\( 400 q - 1600 q^{4} + 2 q^{7} + O(q^{10}) \) \( 400 q - 1600 q^{4} + 2 q^{7} - 42 q^{11} - 30 q^{13} + 6400 q^{16} + 138 q^{17} - 342 q^{19} + 300 q^{22} - 154 q^{23} - 10024 q^{25} - 456 q^{26} - 8 q^{28} - 162 q^{29} - 120 q^{31} - 360 q^{34} - 814 q^{35} - 474 q^{37} - 108 q^{38} - 222 q^{41} + 24 q^{43} + 168 q^{44} + 588 q^{46} - 534 q^{47} - 370 q^{49} + 120 q^{52} - 534 q^{55} - 168 q^{58} - 1992 q^{59} + 942 q^{61} - 25600 q^{64} - 636 q^{65} - 552 q^{68} - 4116 q^{71} + 3402 q^{73} - 288 q^{74} + 1368 q^{76} - 430 q^{77} - 1562 q^{85} - 264 q^{86} - 1200 q^{88} + 8478 q^{91} + 616 q^{92} - 1236 q^{94} + 3018 q^{95} + 2196 q^{97} + 3360 q^{98} + O(q^{100}) \)

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

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