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Properties

Label 2394.4.de
Level $2394$
Weight $4$
Character orbit 2394.de
Rep. character $\chi_{2394}(2003,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $720$
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.de (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 2896 720 2176
Cusp forms 2864 720 2144
Eisenstein series 32 0 32

Trace form

\( 720 q + 2880 q^{4} - 40 q^{6} - 20 q^{9} + O(q^{10}) \) \( 720 q + 2880 q^{4} - 40 q^{6} - 20 q^{9} - 150 q^{11} - 132 q^{15} + 11520 q^{16} + 228 q^{17} - 90 q^{19} - 108 q^{22} - 160 q^{24} + 9000 q^{25} + 720 q^{29} - 448 q^{30} + 324 q^{33} - 80 q^{36} + 636 q^{38} + 1340 q^{39} - 30 q^{41} - 1368 q^{43} - 600 q^{44} - 528 q^{45} - 4560 q^{47} - 17640 q^{49} + 1128 q^{50} + 2070 q^{51} - 1056 q^{53} - 976 q^{54} - 1184 q^{57} + 966 q^{59} - 528 q^{60} - 936 q^{62} - 1288 q^{63} + 46080 q^{64} - 3192 q^{65} + 176 q^{66} + 912 q^{68} - 2724 q^{69} + 414 q^{73} + 1710 q^{75} - 360 q^{76} + 2136 q^{78} - 1516 q^{81} - 1044 q^{82} + 8664 q^{83} + 3968 q^{87} - 432 q^{88} + 1980 q^{89} + 480 q^{90} + 2248 q^{93} - 9780 q^{95} - 640 q^{96} + 1258 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)