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Properties

Label 3420.2.bf
Level $3420$
Weight $2$
Character orbit 3420.bf
Rep. character $\chi_{3420}(1171,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $400$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1472 400 1072
Cusp forms 1408 400 1008
Eisenstein series 64 0 64

Trace form

\( 400 q - 2 q^{4} + O(q^{10}) \) \( 400 q - 2 q^{4} + 6 q^{10} - 24 q^{13} - 2 q^{16} + 8 q^{17} - 200 q^{25} + 4 q^{26} + 20 q^{28} - 30 q^{32} - 42 q^{34} + 10 q^{38} - 48 q^{41} - 40 q^{44} - 344 q^{49} + 78 q^{52} - 24 q^{53} + 4 q^{58} - 32 q^{61} + 8 q^{62} + 16 q^{64} + 52 q^{68} - 36 q^{70} + 12 q^{73} + 68 q^{74} - 16 q^{77} + 38 q^{82} + 16 q^{85} - 12 q^{86} - 36 q^{89} - 80 q^{92} + 12 q^{97} + 54 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \)