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Properties

Label 2394.4.j
Level $2394$
Weight $4$
Character orbit 2394.j
Rep. character $\chi_{2394}(121,\cdot)$
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.j (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

\( 960 q - 1920 q^{4} - 12 q^{7} + O(q^{10}) \) \( 960 q - 1920 q^{4} - 12 q^{7} - 24 q^{13} - 212 q^{15} - 7680 q^{16} - 48 q^{17} + 16 q^{18} - 120 q^{19} - 48 q^{21} + 104 q^{23} - 12000 q^{25} + 264 q^{27} + 96 q^{28} + 136 q^{30} - 60 q^{31} + 552 q^{35} - 168 q^{37} - 698 q^{39} - 2624 q^{41} - 1528 q^{42} - 42 q^{43} - 1592 q^{45} + 66 q^{47} + 240 q^{49} - 152 q^{50} + 800 q^{51} + 192 q^{52} - 704 q^{53} - 120 q^{54} + 916 q^{59} + 160 q^{60} + 840 q^{61} + 256 q^{63} + 61440 q^{64} - 232 q^{65} - 272 q^{66} + 588 q^{67} - 192 q^{68} + 800 q^{69} + 1084 q^{71} + 64 q^{72} - 672 q^{73} + 840 q^{74} + 1250 q^{75} - 480 q^{76} + 2000 q^{77} + 712 q^{78} - 420 q^{79} - 1624 q^{81} - 192 q^{84} + 3496 q^{87} + 4272 q^{89} + 5824 q^{90} - 1500 q^{91} - 208 q^{92} - 888 q^{93} + 2428 q^{95} + 1056 q^{97} + 744 q^{98} + 8376 q^{99} + O(q^{100}) \)

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

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