Properties

Label 2394.2.u
Level $2394$
Weight $2$
Character orbit 2394.u
Rep. character $\chi_{2394}(457,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $288$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.u (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2394, [\chi])\).

Total New Old
Modular forms 976 288 688
Cusp forms 944 288 656
Eisenstein series 32 0 32

Trace form

\( 288 q - 144 q^{4} - 16 q^{5} + 8 q^{6} + 4 q^{9} + O(q^{10}) \) \( 288 q - 144 q^{4} - 16 q^{5} + 8 q^{6} + 4 q^{9} + 16 q^{11} - 4 q^{14} + 8 q^{15} - 144 q^{16} + 16 q^{17} - 8 q^{18} + 8 q^{20} + 16 q^{21} - 24 q^{23} - 4 q^{24} + 288 q^{25} + 32 q^{26} - 24 q^{27} + 20 q^{29} - 4 q^{30} - 4 q^{33} + 4 q^{35} + 16 q^{36} - 24 q^{38} - 16 q^{39} - 20 q^{41} + 8 q^{42} - 8 q^{44} + 36 q^{45} + 12 q^{46} + 6 q^{47} + 24 q^{49} - 32 q^{51} - 32 q^{53} + 2 q^{54} + 24 q^{55} + 8 q^{56} + 24 q^{58} - 16 q^{60} + 12 q^{61} - 88 q^{62} - 62 q^{63} + 288 q^{64} + 20 q^{65} - 32 q^{68} + 4 q^{69} - 16 q^{71} - 8 q^{72} - 12 q^{74} + 60 q^{75} - 20 q^{77} - 48 q^{78} - 36 q^{79} + 8 q^{80} - 36 q^{81} - 32 q^{83} - 20 q^{84} - 24 q^{85} + 48 q^{86} + 32 q^{87} + 24 q^{89} - 12 q^{90} + 12 q^{92} - 20 q^{93} - 24 q^{94} - 4 q^{96} + 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2394, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

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