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Properties

Label 2394.4.cd
Level $2394$
Weight $4$
Character orbit 2394.cd
Rep. character $\chi_{2394}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
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.cd (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

\( 960 q + 1920 q^{4} + 12 q^{7} + O(q^{10}) \) \( 960 q + 1920 q^{4} + 12 q^{7} + 72 q^{13} + 212 q^{15} - 7680 q^{16} - 144 q^{17} + 16 q^{18} - 48 q^{21} - 12000 q^{25} + 96 q^{28} - 136 q^{30} + 168 q^{37} + 278 q^{39} + 904 q^{42} + 42 q^{43} - 696 q^{45} - 198 q^{47} + 240 q^{49} - 456 q^{50} + 800 q^{51} + 1968 q^{57} - 1500 q^{59} + 160 q^{60} + 2520 q^{61} + 700 q^{63} - 61440 q^{64} - 816 q^{66} + 588 q^{67} + 576 q^{68} + 2772 q^{71} - 64 q^{72} + 3354 q^{75} - 3264 q^{77} + 712 q^{78} - 420 q^{79} + 1624 q^{81} + 192 q^{84} + 4656 q^{87} - 180 q^{91} - 624 q^{92} - 2056 q^{93} - 4128 q^{95} - 3168 q^{97} + 2232 q^{98} - 840 q^{99} + O(q^{100}) \)

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

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