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Properties

Label 3420.2.ds
Level $3420$
Weight $2$
Character orbit 3420.ds
Rep. character $\chi_{3420}(407,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2848$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3420.ds (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3420 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3420, [\chi])\).

Total New Old
Modular forms 2912 2912 0
Cusp forms 2848 2848 0
Eisenstein series 64 64 0

Trace form

\( 2848 q - 6 q^{2} - 4 q^{6} + O(q^{10}) \) \( 2848 q - 6 q^{2} - 4 q^{6} - 12 q^{10} + 18 q^{12} - 12 q^{13} + 4 q^{16} - 12 q^{18} - 12 q^{20} - 24 q^{21} - 8 q^{25} + 4 q^{28} + 2 q^{30} - 6 q^{32} - 12 q^{33} - 68 q^{36} - 6 q^{38} - 48 q^{41} - 6 q^{42} - 36 q^{45} - 6 q^{48} - 6 q^{52} + 12 q^{57} + 4 q^{58} - 6 q^{60} - 16 q^{61} - 12 q^{62} + 48 q^{65} - 12 q^{66} + 12 q^{68} + 42 q^{72} - 8 q^{73} + 52 q^{76} - 24 q^{77} - 24 q^{78} + 60 q^{80} - 8 q^{81} - 12 q^{82} + 4 q^{85} - 120 q^{86} - 6 q^{90} - 6 q^{92} - 16 q^{93} - 72 q^{96} - 12 q^{97} - 54 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3420, [\chi])\) into newform subspaces

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