↑

Properties

Label 2394.4.cm
Level $2394$
Weight $4$
Character orbit 2394.cm
Rep. character $\chi_{2394}(977,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
Sturm bound $1920$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2394.cm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
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 960 1936
Cusp forms 2864 960 1904
Eisenstein series 32 0 32

Trace form

\( 960 q - 1920 q^{4} + 12 q^{7} + O(q^{10}) \) \( 960 q - 1920 q^{4} + 12 q^{7} - 120 q^{15} - 7680 q^{16} + 144 q^{17} + 120 q^{19} - 156 q^{23} + 12000 q^{25} + 792 q^{27} - 96 q^{28} - 272 q^{30} - 90 q^{31} - 504 q^{37} - 664 q^{39} + 1060 q^{42} + 84 q^{43} + 448 q^{45} + 240 q^{49} - 1128 q^{50} - 288 q^{52} - 2112 q^{53} + 120 q^{54} - 1220 q^{57} + 3000 q^{59} + 1008 q^{60} + 1680 q^{61} - 26 q^{63} + 61440 q^{64} + 348 q^{65} - 272 q^{66} - 1764 q^{67} - 2772 q^{71} - 672 q^{73} + 1260 q^{74} - 960 q^{76} + 1608 q^{77} - 2136 q^{78} - 1260 q^{79} - 1688 q^{81} + 1640 q^{87} + 2056 q^{93} - 3246 q^{95} + 2232 q^{98} + 8132 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \)