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Properties

Label 2394.4.q
Level $2394$
Weight $4$
Character orbit 2394.q
Rep. character $\chi_{2394}(1075,\cdot)$
Character field $\Q(\zeta_{3})$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1197 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 960 q - 1920 q^{4} - 12 q^{7} + O(q^{10}) \) \( 960 q - 1920 q^{4} - 12 q^{7} + 48 q^{13} + 40 q^{15} - 7680 q^{16} - 48 q^{17} - 32 q^{18} - 120 q^{19} - 48 q^{21} - 52 q^{23} - 12000 q^{25} + 264 q^{27} + 96 q^{28} - 272 q^{30} + 30 q^{31} + 552 q^{35} - 168 q^{37} + 664 q^{39} + 1312 q^{41} - 1060 q^{42} + 84 q^{43} + 448 q^{45} - 132 q^{47} + 240 q^{49} - 152 q^{50} - 1600 q^{51} - 96 q^{52} - 704 q^{53} - 120 q^{54} + 636 q^{57} - 1832 q^{59} + 688 q^{60} - 1680 q^{61} + 1102 q^{63} + 61440 q^{64} + 116 q^{65} - 272 q^{66} + 588 q^{67} + 384 q^{68} + 800 q^{69} + 1084 q^{71} + 64 q^{72} - 672 q^{73} - 420 q^{74} - 2500 q^{75} + 960 q^{76} - 2632 q^{77} + 712 q^{78} - 420 q^{79} + 104 q^{81} + 384 q^{84} + 3208 q^{87} + 4272 q^{89} - 5456 q^{90} - 1500 q^{91} + 416 q^{92} - 888 q^{93} - 2606 q^{95} - 2112 q^{97} + 744 q^{98} - 6396 q^{99} + O(q^{100}) \)

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

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