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Properties

Label 3420.2.dc
Level $3420$
Weight $2$
Character orbit 3420.dc
Rep. character $\chi_{3420}(2729,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
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.dc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
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 1464 240 1224
Cusp forms 1416 240 1176
Eisenstein series 48 0 48

Trace form

\( 240 q + O(q^{10}) \) \( 240 q + 21 q^{15} + 48 q^{45} + 120 q^{49} + 24 q^{51} - 36 q^{59} - 30 q^{65} + 24 q^{69} + 18 q^{71} + 9 q^{75} + 32 q^{81} - 48 q^{95} + 12 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1710, [\chi])\)\(^{\oplus 2}\)