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Properties

Label 2394.4.ce
Level $2394$
Weight $4$
Character orbit 2394.ce
Rep. character $\chi_{2394}(761,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $864$
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.ce (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 864 2032
Cusp forms 2864 864 2000
Eisenstein series 32 0 32

Trace form

\( 864 q - 3456 q^{4} - 120 q^{9} + O(q^{10}) \) \( 864 q - 3456 q^{4} - 120 q^{9} + 48 q^{11} + 264 q^{14} + 80 q^{15} + 13824 q^{16} - 224 q^{18} - 384 q^{21} - 504 q^{23} - 10800 q^{25} - 240 q^{26} + 900 q^{27} - 84 q^{29} - 448 q^{30} + 1560 q^{35} + 480 q^{36} - 910 q^{39} + 1236 q^{41} + 508 q^{42} - 192 q^{44} + 660 q^{45} + 504 q^{46} - 396 q^{47} - 396 q^{49} - 400 q^{51} + 2184 q^{53} - 180 q^{54} - 1056 q^{56} + 504 q^{58} - 320 q^{60} - 5904 q^{62} - 1070 q^{63} - 55296 q^{64} + 2400 q^{66} - 3696 q^{69} + 648 q^{70} + 896 q^{72} - 1260 q^{74} - 5640 q^{75} - 6312 q^{77} - 2144 q^{78} + 3240 q^{79} - 2792 q^{81} + 1536 q^{84} - 1440 q^{85} + 2400 q^{86} - 624 q^{87} + 8796 q^{89} + 5976 q^{90} + 2016 q^{92} + 4328 q^{93} + 2208 q^{98} + 4608 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)