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Properties

Label 3420.2.cr
Level $3420$
Weight $2$
Character orbit 3420.cr
Rep. character $\chi_{3420}(1471,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
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.cr (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 684 \)
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 1456 960 496
Cusp forms 1424 960 464
Eisenstein series 32 0 32

Trace form

\( 960 q + 8 q^{9} + O(q^{10}) \) \( 960 q + 8 q^{9} + 8 q^{17} - 16 q^{24} - 480 q^{25} - 16 q^{26} + 16 q^{30} + 18 q^{34} - 28 q^{36} - 20 q^{38} + 60 q^{41} + 18 q^{42} - 6 q^{44} + 66 q^{48} + 480 q^{49} - 14 q^{54} + 120 q^{56} + 16 q^{57} - 88 q^{62} + 24 q^{64} + 28 q^{66} + 84 q^{72} + 12 q^{73} - 56 q^{74} + 6 q^{76} - 60 q^{78} - 8 q^{80} - 40 q^{81} + 30 q^{84} - 32 q^{92} + 112 q^{96} + 66 q^{98} + O(q^{100}) \)

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

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