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Properties

Label 2394.4.ek
Level $2394$
Weight $4$
Character orbit 2394.ek
Rep. character $\chi_{2394}(253,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $900$
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.ek (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1920\)

Dimensions

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

Total New Old
Modular forms 8736 900 7836
Cusp forms 8544 900 7644
Eisenstein series 192 0 192

Trace form

\( 900 q + 48 q^{8} + O(q^{10}) \) \( 900 q + 48 q^{8} + 384 q^{17} + 432 q^{22} - 468 q^{23} + 1068 q^{25} + 672 q^{29} - 60 q^{31} + 168 q^{35} + 888 q^{37} - 324 q^{38} + 630 q^{41} - 1872 q^{43} + 1200 q^{44} - 456 q^{46} + 1032 q^{47} - 22050 q^{49} + 2100 q^{50} - 3984 q^{53} - 5904 q^{55} - 1344 q^{56} - 2592 q^{58} + 1230 q^{59} - 3456 q^{61} - 1824 q^{62} - 28800 q^{64} + 4080 q^{65} + 786 q^{67} + 456 q^{68} + 3024 q^{70} + 2172 q^{71} + 3624 q^{73} - 696 q^{74} - 2220 q^{79} + 1740 q^{82} + 2412 q^{83} - 5460 q^{85} + 3888 q^{86} - 1056 q^{88} + 4008 q^{89} + 1584 q^{92} + 11232 q^{95} + 2202 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)